A000162 -id:A000162 - cp's OEIS frontend

A038119 Number of n-celled solid polyominoes (or free polycubes, allowing mirror-image identification).

1, 1, 2, 7, 23, 112, 607, 3811, 25413, 178083, 1279537, 9371094, 69513546, 520878101, 3934285874, 29915913663, 228779330204, 1758309223457, 13573319825615, 105192814197984, 818136047201932, 6383528588447574

Offset: 1

N. J. A. Sloane

a(1)-a(12) computed by Achim Flammenkamp.
A000162 but with one copy of each mirror-image deleted.
From R. J. Mathar, Mar 19 2018: (Start)
We can split the numbers into an irregular table which lists in row n how many configurations have c contacts for c >= 0:
  1;
  0 1;
  0 0 2;
  0 0 0 6 1;
  0 0 0 0 21 2;
  0 0 0 0 0 91 19 2;
  0 0 0 0 0 0 484 110 12 1;
  0 0 0 0 0 0 0 2817 852 129 12 0 1;
  0 0 0 0 0 0 0 0 17788 6321 1166 132 5 1;
Row lengths are 1+A007818(n). Row sums are a(n).
(End)
Number of unoriented polyominoes with n cubical cells of the regular tiling with Schläfli symbol {4,3,4}. For unoriented polyominoes, chiral pairs are counted as one.- Robert A. Russell, Mar 21 2024

S. W. Golomb, Polyominoes. Scribner's, NY, 1965; second edition (Polyominoes: Puzzles, Packings, Problems and Patterns) Princeton Univ. Press, 1994.
W. F. Lunnon, Symmetry of cubical and general polyominoes, pp. 101-108 of R. C. Read, editor, Graph Theory and Computing. Academic Press, NY, 1972. [See https://books.google.nl/books?id=ja7iBQAAQBAJ&pg=PA101]
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Achim Flammenkamp, Home page.
Kevin L. Gong, Polyominoes Home Page.
John Mason, Counting free polycubes.
John Mason, Coordinate sets of examples of polycube symmetry (version 2)

A038119 = (A007743+A000162)/2, A007743 = 2*A038119 - A000162, A000162 = 2*A038119 - A007743.
32nd row of A366766.
Cf. A000162 (oriented), A371397 (chiral), A007743 (achiral), A001931 (fixed).
Cf. for each symmetry: A376964, A376965, A376966, A376967, A376968, A376969, A376970, A376972, A376973, A376974, A376975, A376976, A376977, A376978, A376979, A376980, A376981, A376982, A376983, A377127, A376984, A376985, A376986, A376987, A376988, A376989, A377128, A376990, A376991, A377129, A377130, A377131, A376971

A[s_Integer] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[ Import["https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {, }][[All, 2]]];
A000162 = A@000162;
A007743 = A@007743;
a[n_] := (A007743[[n]] + A000162[[n]])/2;
a /@ Range[16] (* Jean-François Alcover, Jan 16 2020 *)

a(n) = A000162(n) - A371397(n) = A371397(n) + A007743(n). - Robert A. Russell, Mar 21 2024

More terms from Brendan Owen (brendan_owen(AT)yahoo.com), Jan 02 2002
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 05 2007
More terms from John Mason, Sep 19 2024

A006983 Number of simple perfect squared squares of order n up to symmetry.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 8, 12, 26, 160, 441, 1152, 3001, 7901, 20566, 54541, 144161, 378197, 990981, 2578081, 6674067, 17086918

Offset: 1

N. J. A. Sloane

A squared rectangle (which may be a square) is a rectangle dissected into a finite number of two or more squares. If no two squares have the same size, the squared rectangle is perfect. A squared rectangle is simple if it does not contain a smaller squared rectangle. The order of a squared rectangle is the number of constituent squares. - Geoffrey H. Morley, Oct 17 2012

J.-P. Delahaye, Les inattendus mathématiques, Belin-Pour la Science, Paris, 2004, pp. 95-96.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Stuart E. Anderson, Perfect Squared Rectangles and Squared Squares
Stuart E. Anderson, Simple perfect squared squares in orders 27 to 37 - methods used and people involved.
C. J. Bouwkamp, On some new simple perfect squared squares, Discrete Math. 106-107 (1992) 67-75.
C. J. Bouwkamp and A. J. W. Duijvestijn, Catalogue of Simple Perfect Squared Squares of orders 21 through 25, EUT Report 92-WSK-03, Eindhoven University of Technology, Eindhoven, The Netherlands, November 1992.
C. J. Bouwkamp and A. J. W. Duijvestijn, Album of Simple Perfect Squared Squares of order 26, EUT Report 94-WSK-02, Eindhoven University of Technology, Eindhoven, The Netherlands, December 1994.
C. J. Bouwkamp, A. J. W. Duijvestijn, & N. J. A. Sloane, Correspondence, 1971.
G. Brinkmann and B. D. McKay, Fast generation of planar graphs, MATCH Commun. Math. Comput. Chem., 58 (2007), 323-357.
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph.
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph [Cached copy, pdf file only, no active links, with permission]
A. J. W. Duijvestijn, Illustration for a(21)=1 (The unique simple squared square of order 21. Reproduced with permission of the discoverer.)
A. J. W. Duijvestijn, Simple perfect squared squares and 2x1 squared rectangles of orders 21 to 24, J. Combin. Theory Ser. B 59 (1993), 26-34.
A. J. W. Duijvestijn, Simple perfect squared squares and 2x1 squared rectangles of order 25, Math. Comp. 62 (1994), 325-332. doi:10.1090/S0025-5718-1994-1208220-9
A. J. W. Duijvestijn, Simple perfect squares and 2x1 squared rectangles of order 26, Math. Comp. 65 (1996), 1359-1364. doi:10.1090/S0025-5718-96-00705-3 [TableI List of Simple Perfect Squared Squares of order 26 and TableII List of Simple Perfect Squared 2x1 Rectangles of order 26 are now on squaring.net and no longer located as described in the paper.]
I. Gambini, Quant aux carrés carrelés, Thesis, Université de la Méditerranée Aix-Marseille II, 1999, p. 25.
Ed Pegg Jr., Advances in Squared Squares, Wolfram Community Bulletin, Jul 23 2020
Eric Weisstein's World of Mathematics, Perfect Square Dissection
Index entries for squared squares

Cf. A002962, A002881, A002839, A014530.
Cf. A181340, A181735, A217155, A217156.
Cf. A129947, A217149, A228953 (related to sizes of the squares).
Cf. A349205, A349206, A349207, A349208, A349209, A349210 (related to ratios of element and square sizes).

Leading term changed from 0 to 1, Apr 15 1996
More terms from Stuart E Anderson, May 08 2003, Nov 2010
Leading term changed back to 0, Dec 25 2010 (cf. A178688)
a(29) added by Stuart E Anderson, Aug 22 2010; contributors to a(29) include Ed Pegg Jr and Stephen Johnson
a(29) changed to 7901, identified a duplicate tiling in order 29. - Stuart E Anderson, Jan 07 2012
a(28) changed to 3000, identified a duplicate tiling in order 28. - Stuart E Anderson, Jan 14 2012
a(28) changed back to 3001 after a complete recount of order 28 SPSS recalculated from c-nets with cleansed data, established the correct total of 3001. - Stuart E Anderson, Jan 24 2012
Definition clarified by Geoffrey H. Morley, Oct 17 2012
a(30) added by Stuart E Anderson, Apr 10 2013
a(31), a(32) added by Stuart E Anderson, Sep 29 2013
a(33), a(34) and a(35) added by Stuart E Anderson, May 02 2016
Moved comments on orders 27 to 35 to a linked file.  Stuart E Anderson, May 02 2016
a(36) and a(37) enumerated by Jim Williams, added by Stuart E Anderson, Jul 26 2020.

A038173 Number of "connected animals" formed from n rhombic dodecahedra (or edge-connected cubes) in the face-centered cubic lattice, allowing translation and rotations of the lattice and reflections.

Original entry on oeis.org

1, 1, 4, 20, 131, 1211, 12734, 144158, 1687737, 20196788, 245366931, 3016835487

Offset: 1

Achim Flammenkamp

This extends earlier work of Torsten Sillke (torsten.sillke(AT)lhsystems.com).

S. T. Coffin, Puzzling World of Polyhedral Dissections, Oxford Univ. Press, 1991.
George Sicherman, Catalogue of Polyrhons
T. Sillke, Notations for polyspheres
Index entries for sequences related to f.c.c. lattice

Cf. A000162, A038119 (for simple-cubic lattice), A038168-A038174, A300812 (refined by number of contacts).

33rd row of A366766.

a(10) from George Sicherman, Jul 24 2012
a(11) from Joerg Arndt and Márk Péter Légrádi, Apr 30 2023
a(12) from Bert Dobbelaere, Jun 26 2025

A038181 Number of "connected animals" formed from n 4-gon or 6-gon connected truncated octahedra in the b.c.c. lattice, allowing translation and rotations of the lattice and reflections.

Original entry on oeis.org

1, 2, 6, 35, 251, 2602, 30900, 400818, 5401599, 74617105, 1047497078, 14888851869

Offset: 1

Torsten Sillke (TORSTEN.SILLKE(AT)LHSYSTEMS.COM)

These are "free polyforms" consisting of face-connected polyhedral cells in the bitruncated cubic honeycomb. - Peter Kagey, Jun 23 2025

S. T. Coffin, Puzzling World of Polyhedral Dissections, Oxford Univ. Press, 1991.
M. Owen, Splatts
T. Sillke, Notations for polyspheres
Index entries for sequences related to b.c.c. lattice
Wikipedia, Bitruncated cubic honeycomb

Cf. A000162, A038119, A038168-A038174, A038180, A038386.

More terms from Achim Flammenkamp
Definition corrected by Fred Bayer, Aug 11 2010
More terms from Mark Owen, Oct 11 2013

A384254 Number of connected components of n polyhedra in the rectified cubic honeycomb up to translation, rotation, and reflection of the honeycomb.

Original entry on oeis.org

1, 2, 2, 9, 40, 290, 2529, 26629, 301289, 3568048, 43305326, 534671742, 6684869463

Offset: 0

Peter Kagey, May 23 2025

Equivalently the number of connected components of n polyhedra in the truncated cubic honeycomb up to translation, rotation, and reflection of the honeycomb.

			For n=1, the a(1)=2 different components are the cuboctahedron and the octahedron.
For n=2, the a(2)=1 component is a cuboctahedron connected to an octahedron.
For n=3, there are A000162(3)=2 components that consist of three cuboctahedra, four connected components that consist of two cuboctahedra and an octahedron, and three components that consist of a cuboctahedron and two octahedra.

Peter Kagey, Illustration of a(3)=9.
Wikipedia, Convex uniform honeycomb

Cf. A038119 (cubic honeycomb), A038181 (bitruncated cubic honeycomb), A343577 (truncated square tiling), A343909 (tetrahedral-octahedral honeycomb), A384274 (rectified cubic honeycomb).

a(8)-a(12) from Bert Dobbelaere, Jun 09 2025

A001931 Number of fixed 3-dimensional polycubes with n cells; lattice animals in the simple cubic lattice (6 nearest neighbors), face-connected cubes.

Original entry on oeis.org

1, 3, 15, 86, 534, 3481, 23502, 162913, 1152870, 8294738, 60494549, 446205905, 3322769321, 24946773111, 188625900446, 1435074454755, 10977812452428, 84384157287999, 651459315795897, 5049008190434659, 39269513463794006, 306405169166373418

Offset: 1

N. J. A. Sloane

This gives the number of polycubes up to translation (but not rotation or reflection). - Charles R Greathouse IV, Oct 08 2013

W. F. Lunnon, Symmetry of cubical and general polyominoes, pp. 101-108 of R. C. Read, editor, Graph Theory and Computing. Academic Press, NY, 1972.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

G. Aleksandrowicz and G. Barequet, Counting d-dimensional polycubes and nonrectangular planar polyominoes, Computing and Combinatorics, 12th Annual International Conference, COCOON 2006, Taipei, Taiwan, August 15-18, 2006, pp. 418-427.
G. Aleksandrowicz and G. Barequet, Counting d-dimensional polycubes and nonrectangular planar polyominoes, Int. J. of Computational Geometry and Applications, 19 (2009), 215-229.
A. Asinowski, G. Barequet, and Y. Zheng, Polycubes with small perimeter defect, Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, (2018).
Gill Barequet, Gil Ben-Shachar, and Martha Carolina Osegueda, Applications of Concatenation Arguments to Polyominoes and Polycubes, EuroCG '20, 36th European Workshop on Computational Geometry, (Würzburg, Germany, 16-18 March 2020).
Gill Barequet, Solomon W. Golomb, and David A. Klarner, Polyominoes. (This is a revision, by G. Barequet, of the chapter of the same title originally written by the late D. A. Klarner for the first edition, and revised by the late S. W. Golomb for the second edition.) Preprint, 2016.
Andrew R. Conway, The design of efficient dynamic programming and transfer matrix enumeration algorithms, Journal of Physics A: Mathematical and Theoretical, 2 August 2017. For another version see arXiv, arXiv:1610.09806 [math.CO], 2016-2017.
Stanley Dodds, C# program for this sequence
Kevin L. Gong, Polyominoes Home Page
S. Luther and S. Mertens, Counting lattice animals in high dimensions, Journal of Statistical Mechanics: Theory and Experiment, 2011 (9), 546-565; arXiv:1106.1078 [cond-mat.stat-mech], 2011.
S. Mertens, Lattice animals: a fast enumeration algorithm and new perimeter polynomials, J. Stat. Phys. 58 (5-6) (1990) 1095-1108, Table 1.
H. Redelmeier, Emails to N. J. A. Sloane, 1991
Phillip Thompson, rust port of Dodds's C# program

Cf. A000162, A001420, A038119 (free), A151830, A151832, A151833, A151834, A151835.

32nd row of A366767.

Edited by Arun Giridhar, Feb 14 2011
a(17) from Achim Flammenkamp, Feb 15 1999
a(18) from the Aleksandrowicz and Barequet paper (N. J. A. Sloane, Jul 09 2009)
a(19) from Luther and Mertens by Gill Barequet, Jun 12 2011
a(20) from Stanley Dodds, Aug 03 2023
a(21)-a(22) (using Dodds's algorithm) from Phillip Thompson, Feb 07 2024

A002839 Number of simple perfect squared rectangles of order n up to symmetry.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 22, 67, 213, 744, 2609, 9016, 31426, 110381, 390223, 1383905, 4931308, 17633773, 63301427, 228130926, 825229110, 2994833854

Offset: 1

N. J. A. Sloane

A squared rectangle is a rectangle dissected into a finite number of integer-sized squares. If no two of these squares are the same size then the squared rectangle is perfect. A squared rectangle is simple if it does not contain a smaller squared rectangle or squared square. The order of a squared rectangle is the number of squares into which it is dissected. [Edited by Stuart E Anderson, Feb 03 2024]

See A217156 for further references and links.
C. J. Bouwkamp, personal communication.
C. J. Bouwkamp, A. J. W. Duijvestijn and P. Medema, Catalogue of simple squared rectangles of orders nine through fourteen and their elements, Technische Hogeschool, Eindhoven, The Netherlands, May 1960, 50 pp.
C. J. Bouwkamp, A. J. W. Duijvestijn and J. Haubrich, Catalogue of simple perfect squared rectangles of orders 9 through 18, Philips Research Laboratories, Eindhoven, The Netherlands, 1964 (unpublished) vols 1-12, 3090 pp.
A. J. W. Duijvestijn, Fast calculation of inverse matrices occurring in squared rectangle calculation, Philips Res. Rep. 30 (1975), 329-339.
M. E. Lines, Think of a Number, Institute of Physics, London, 1990, p. 43.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
W. T. Tutte, Squaring the Square, in M. Gardner's 'Mathematical Games' column in Scientific American 199, Nov. 1958, pp. 136-142, 166. Reprinted with addendum and bibliography in the US in M. Gardner, The 2nd Scientific American Book of Mathematical Puzzles & Diversions, Simon and Schuster, New York (1961), pp. 186-209, 250 [sequence p. 207], and in the UK in M. Gardner, More Mathematical Puzzles and Diversions, Bell (1963) and Penguin Books (1966), pp. 146-164, 186-7 [sequence p. 162].

S. E. Anderson, Perfect Squared Rectangles and Squared Squares.
C. J. Bouwkamp, On the dissection of rectangles into squares (Papers I-III), Koninklijke Nederlandsche Akademie van Wetenschappen, Proc., Ser. A, Paper I, 49 (1946), 1176-1188 (=Indagationes Math., v. 8 (1946), 724-736); Paper II, 50 (1947), 58-71 (=Indagationes Math., v. 9 (1947), 43-56); Paper III, 50 (1947), 72-78 (=Indagationes Math., v. 9 (1947), 57-63).
C. J. Bouwkamp, On the construction of simple perfect squared squares, Koninklijke Nederlandsche Akademie van Wetenschappen, Proc., Ser. A, 50 (1947), 1296-1299 (=Indagationes Math., v. 9 (1947), 622-625).
C. J. Bouwkamp and A. J. W. Duijvestijn, Catalogue of Simple Perfect Squared Squares of orders 21 through 25, EUT Report 92-WSK-03, Eindhoven University of Technology, Eindhoven, The Netherlands, November 1992.
C. J. Bouwkamp, A. J. W. Duijvestijn and P. Medema, Tables relating to simple squared rectangles of orders nine through fifteen, Technische Hogeschool, Eindhoven, The Netherlands, August 1960, ii + 360 pp. Reprinted in EUT Report 86-WSK-03, January 1986. [Sequence p. i.]
C. J. Bouwkamp & N. J. A. Sloane, Correspondence, 1971.
R. L. Brooks, C. A. B. Smith, A. H. Stone and W. T. Tutte, The dissection of rectangles into squares, Duke Math. J., 7 (1940), 312-340. Reprinted in I. Gessel and G.-C. Rota (editors), Classic papers in combinatorics, Birkhäuser Boston, 1987, pp. 88-116. [Pp. 324-5 of the original article have counts up to a(12).]
A. J. W. Duijvestijn, Electronic Computation of Squared Rectangles, Thesis, Technische Hogeschool, Eindhoven, Netherlands, 1962. Reprinted in Philips Res. Rep. 17 (1962), 523-612.
I. Gambini, Quant aux carrés carrelés, Thesis, Université de la Méditerranée Aix-Marseille II, 1999, p. 24. [Number of simple rectangles excludes squares in separate column (from order 21).]
D. Moews, Squared rectangles
W. T. Tutte, A Census of Planar Maps, Canad. J. Math. 15 (1963), 249-271.
J. H. van Lint, Letter to N. J. A. Sloane, N.D.
Eric Weisstein's World of Mathematics, Perfect Square Dissection.
Index entries for squared rectangles
Index entries for squared squares

Cf. A006983, A002962, A002881, A181735.

Cf. A217153, A217154, A217156, A219766.

From Stuart E Anderson, Mar 02 2011, Feb 03 2024: (Start)
In "A Census of Planar Maps", p. 267, William Tutte gave a conjectured asymptotic formula for the number of perfect squared rectangles where n is the number of elements in the dissection (the order):
Conjecture: a(n) ~ n^(-5/2) * 4^n / (243*sqrt(Pi)). (End)
a(n) = A006983(n) + A219766(n). - Stuart E Anderson, Dec 07 2012

Definition corrected to include 'simple'. 'Simple' and 'perfect' defined in comments. - Geoffrey H. Morley, Mar 11 2010
Corrected a(18) and extended terms to order 21.  All 3-connected planar graphs up to 22 edges used to generate dissections. Imperfect squared rectangles, compound squared rectangles, and all squared squares filtered out leaving simple perfect squared rectangles. - Stuart E Anderson, Mar 2011
Corrected a(18) to a(21) after removing last remaining compounds. - Stuart E Anderson, Apr 10 2011
Added a(22), a(23) and a(24) from Ian Gambini's thesis and corrected a(22). Added I. Gambini's thesis reference. - Stuart E Anderson, May 08 2011
Added some additional references, previous correction to a(22) is an increase of 4 based on a new count of order 22. - Stuart E Anderson, Jul 13 2012
Terms a(21)-a(24) corrected to include squares by Geoffrey H. Morley, Oct 17 2012
a(22)=17633773 from Stuart E Anderson confirmed by Geoffrey H. Morley, Nov 28 2012
a(23)-a(24) from Gambini confirmed by Stuart E Anderson, Dec 07 2012
a(25) from Stuart E Anderson, May 07 2024
a(26) from Stuart E Anderson, Jul 28 2024

A002840 Number of polyhedral graphs with n edges.

Original entry on oeis.org

1, 0, 1, 2, 2, 4, 12, 22, 58, 158, 448, 1342, 4199, 13384, 43708, 144810, 485704, 1645576, 5623571, 19358410, 67078828, 233800162, 819267086, 2884908430, 10204782956, 36249143676, 129267865144, 462669746182, 1661652306539, 5986979643542

Offset: 6

N. J. A. Sloane

M. B. Dillencourt, Polyhedra of small orders and their Hamiltonian properties. Tech. Rep. 92-91, Info. and Comp. Sci. Dept., Univ. Calif. Irvine, 1992.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
T. R. S. Walsh, personal communication.

C. J. Bouwkamp & N. J. A. Sloane, Correspondence, 1971
A. J. W. Duijvestijn and P. J. Federico, The number of polyhedral (3-connected planar) graphs, Math. Comp. 37 (1981), no. 156, 523-532.
P. J. Federico, Enumeration of polyhedra: the number of 9-hedra, J. Combin. Theory, 7 (1969), 155-161.
G. P. Michon, Counting Polyhedra - Numericana
Hugo Pfoertner, Unlabeled 3-connected planar graphs for n<=20 edges, list in PARI-readable format.
Eric Weisstein's World of Mathematics, Polyhedral Graph
T. R. S. Walsh, Number of sensed planar maps with n edges and m vertices

Column sums of A049337.

Cf. A002841, A000944, A046091, A338511, A343869, A343871.

\\ It is assumed that the 3cp.gp file (from the linked zip archive) has been read before, i.e., \r [path]3cp.gp
for(k=6,#ThreeConnectedData,print1(#ThreeConnectedData[k],", "));
\\ printing of the edge lists of the graphs for n <= 11
print(ThreeConnectedData[6..11]) \\ Hugo Pfoertner, Feb 14 2021

a(30)-a(35) from the Numericana link added by Andrey Zabolotskiy, Jun 13 2020

A002962 Number of simple imperfect squared squares of order n up to symmetry.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 5, 15, 19, 57, 72, 274, 491, 1766, 3679, 11158, 24086, 64754, 132598, 326042, 667403, 1627218, 3508516

Offset: 1

N. J. A. Sloane

A squared rectangle (which may be a square) is a rectangle dissected into a finite number, two or more, of squares. If no two of these squares have the same size the squared rectangle is perfect. A squared rectangle is simple if it does not contain a smaller squared rectangle. The order of a squared rectangle is the number of constituent squares. - Geoffrey H. Morley, Oct 17 2012

Orders 15 to 19 were enumerated by C. J. Bowkamp and A. J. W. Duijvestijn (1962). Orders 20 to 29 were enumerated by Stuart Anderson (2010-2012). Orders 30 to 32 were enumerated by Lorenz Milla and Stuart Anderson (2013). - Stuart E Anderson, Sep 30 2013

C. J. Bouwkamp, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Stuart Anderson, Simple Imperfect Squared Squares.
C. J. Bouwkamp & N. J. A. Sloane, Correspondence, 1971
A. J. W. Duijvestijn, Electronic Computation of Squared Rectangles, Thesis, Technische Hogeschool, Eindhoven, Netherlands, 1962. Reprinted in Philips Res. Rep., 17 (1962), 523-612. [Pp. 573-4 have simple imperfect squares up to order 19.]
Index entries for squared squares

Cf. A002839, A002881, A006983, A014530.

Cf. A181735, A217155, A217156.

a(19) corrected and terms extended up to a(22) by Stuart E Anderson, Mar 08 2011
a(21) and a(22) corrected and terms extended to a(25) by Stuart E Anderson, Apr 24 2011
a(21), a(22), a(25) corrected and a(26)-a(28) added by Stuart E Anderson, Jul 11 2011
a(29) from Stuart E Anderson, Ed Pegg Jr, Stephen Johnson, Aug 22 2011
a(29) corrected by Stuart E Anderson, Aug 24 2011
Definition clarified and offset changed to 1 by Geoffrey H. Morley, Oct 17 2012
a(28) corrected by Stuart E Anderson, Dec 01 2012
a(30) from Lorenz Milla and Stuart E Anderson, Apr 10 2013
a(26) and a(29) corrected by Stuart E Anderson, Aug 20 2013
a(31), a(32) from Lorenz Milla and Stuart E Anderson, Sep 30 2013

A038168 Number of "connected animals" formed from n tricapped truncated tetrahedra in the diamond lattice, allowing translation and rotations of the lattice.

Original entry on oeis.org

1, 1, 1, 4, 10, 39, 160, 726, 3344, 16004, 77323, 379117, 1874540

Offset: 1

Achim Flammenkamp

nonn

S. T. Coffin, Puzzling World of Polyhedral Dissections, Oxford Univ. Press, 1991.

Cf. A000162, A038119, A038169-A038174.

cp's OEIS Frontend

A038119 Number of n-celled solid polyominoes (or free polycubes, allowing mirror-image identification).

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A006983 Number of simple perfect squared squares of order n up to symmetry.

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A038173 Number of "connected animals" formed from n rhombic dodecahedra (or edge-connected cubes) in the face-centered cubic lattice, allowing translation and rotations of the lattice and reflections.

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A038181 Number of "connected animals" formed from n 4-gon or 6-gon connected truncated octahedra in the b.c.c. lattice, allowing translation and rotations of the lattice and reflections.

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A384254 Number of connected components of n polyhedra in the rectified cubic honeycomb up to translation, rotation, and reflection of the honeycomb.

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A001931 Number of fixed 3-dimensional polycubes with n cells; lattice animals in the simple cubic lattice (6 nearest neighbors), face-connected cubes.

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A002839 Number of simple perfect squared rectangles of order n up to symmetry.

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A002840 Number of polyhedral graphs with n edges.

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A002962 Number of simple imperfect squared squares of order n up to symmetry.

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