A000228 -id:A000228 - cp's OEIS frontend

A120102 Number of polyominoes consisting of 8 regular unit n-gons.

66, 369, 2812, 1448, 2876, 10102, 34838, 73675, 181127, 131801, 185297, 352375, 725869, 1180526, 2104485, 1694978, 2123088, 3291481, 5402087, 7739008, 11832175, 10079003, 11917261, 16624712, 24389611, 32317393, 45260884

Offset: 3

Sascha Kurz, Jun 09 2006

nonn

			a(3)=66 because there are 66 polyiamonds consisting of 8 triangles and a(4)=369 because there are 369 polyominoes consisting of 8 squares.

Matthias Koch and Sascha Kurz, Enumeration of generalized polyominoes, preprint, arXiv:math/0605144 [math.CO], 2006.

Cf. A000577, A000104, A000228, A103465, A103466, A103467, A103468, A103469, A103470, A103471, A103472, A103473, A103465, A120103, A120104.

A120104 Number of polyominoes consisting of 10 regular unit n-gons.

Original entry on oeis.org

448, 4655, 76092, 30490, 80075, 430302, 2285047, 6078768, 20376032, 13303523, 21208739, 49734303, 131517548, 249598727, 540742895, 404616118, 549711709, 983715865, 1910489463, 3070327312

Offset: 3

Sascha Kurz, Jun 09 2006

nonn

			a(3)=448 because there are 448 polyiamonds consisting of 10 triangles;
a(4)=4655 because there are 4655 polyominoes consisting of 10 squares.

Matthias Koch and Sascha Kurz, Enumeration of generalized polyominoes, preprint arXiv:math/0605144 [math.CO], 2006.

Cf. A000577, A000104, A000105, A000228, A103465 - A103473, A103465, A120102, A120103.

A323930 Polycyclic aromatic hydrocarbons (for precise definition see He and He, 1986).

Original entry on oeis.org

1, 1, 3, 7, 22, 81, 331, 1436, 6510, 30129, 141512, 671538, 3210620, 15443871, 74662005, 362506902

Offset: 1

N. J. A. Sloane, Feb 09 2019

N. Trinajstić, S. Nikolić, J. V. Knop, W. R. Müller and K. Szymanski, Computational Chemical Graph Theory: Characterization, Enumeration, and Generation of Chemical Structures by Computer Methods, Ellis Horwood, 1991. [incorrectly gives a(12) = 671512 in Table 4.13]

Björg N. Cyvin, Jon Brunvoll and Sven J. Cyvin, Enumeration of benzenoid systems and other polyhexes, p. 65-180 in: I. Gutman (ed.), Advances in the Theory of Benzenoid Hydrocarbons II, Springer, 1992.
Wenchen He and Wenjie He, Generation and enumeration of planar polycyclic aromatic hydrocarbons, Tetrahedron 42.19 (1986): 5291-5299. See Table 1.
Lorentz Jäntschi, Topological Characterization of a Complete Set of Small‐Sized Graphene Sheets Using Molecular Descriptors With Energy Storage Applications, Ener. Stor. (2025) Vol. 7, Issue 6, Art No. e70253.

Cf. A003104, A323923-A323929.
A018190 is a very similar sequence with (as He and He remark) a slightly different definition. Cf. A000228, A038147.
Cf. A038140, A038141.

a(n) = A018190(n) + A038140(n) + A038141(n). - Andrey Zabolotskiy, Feb 16 2023

a(10)-a(16) from Cyvin, Brunvoll & Cyvin (Table 1) added by Andrey Zabolotskiy, Feb 08 2023

A005963 Number of restricted hexagonal polyominoes with n cells.

Original entry on oeis.org

0, 0, 1, 2, 10, 45, 210, 1002, 4883, 23797, 116518, 571471

Offset: 1

N. J. A. Sloane

nonn

A. T. Balaban, Enumeration of Cyclic Graphs, pp. 63-105 of A. T. Balaban, ed., Chemical Applications of Graph Theory, Ac. Press, 1976; see p. 75.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Equals A000228 - A002216.

Cf. A036359, A002216, A005963, A000228, A001998.

A036359 Number of branched catafusenes with n condensed hexagons.

Original entry on oeis.org

0, 0, 0, 1, 2, 12, 53, 250, 1115, 5012, 22032, 96746, 422732, 1848128, 8088090, 35498533, 156328706, 691192578, 3068780449, 13683070474, 61267204610, 275455737555, 1243320744572, 5633022679582, 25611815936218, 116840427373176, 534705818846660, 2454282243059471

Offset: 1

N. J. A. Sloane

nonn

F. Harary and R. C. Read, The Enumeration of Tree-like Polyhexes, Proc. Edinburgh Math. Soc., Series II, 17 (1970), pp. 1-13.
Alexandru T. Balaban, The Enumeration of Cyclic Graphs, pp. 63-105 of A. T. Balaban, ed., Chemical Applications of Graph Theory, Ac. Press, 1976; see p. 75.

Cf. A036359, A002216, A005963, A000228, A001998.

a(n) = A002216(n) - A001998(n-2) with A001998(-1)=1. - Sean A. Irvine, Oct 26 2020

More terms from Sean A. Irvine, Oct 26 2020

A103468 Number of polyominoes consisting of n regular unit 10-gons.

Original entry on oeis.org

1, 1, 4, 19, 127, 985, 8350, 73675, 664411, 6078768, 56198759, 523924389, 4918127659

Offset: 1

Sascha Kurz, Feb 07 2005

Matthias Koch and Sascha Kurz, Enumeration of generalized polyominoes, arXiv:math.CO/0605144
S. Kurz, k-polyominoes.

Cf. A000577, A000104, A000228, A103465 - A103473, A115071, A120102 - A120104.

More terms from Sascha Kurz, Jun 09 2006

A120103 Number of polyominoes consisting of 9 regular unit n-gons.

Original entry on oeis.org

160, 1285, 14445, 6572, 14982, 65323, 280014, 664411, 1908239, 1314914, 1968684, 4158216, 9707046, 17054708, 33522023, 26019735, 33942901, 56537856, 100952307, 153177526, 251530341, 208524646, 254079408, 374310135, 586169115, 812395658

Offset: 3

Sascha Kurz, Jun 09 2006

nonn

			a(3)=160 because there are 160 polyiamonds consisting of 9 triangles and a(4)=1285 because there are 1285 polyominoes consisting of 9 squares.

Matthias Koch and Sascha Kurz, Enumeration of generalized polyominoes, preprint, arXiv:math.CO/0605144

Cf. A000577, A000104, A000105, A000228, A103465, A103466, A103467, A103468, A103469, A103470, A103471, A103472, A103473, A103465, A120102, A120104.

A103466 Number of polyominoes consisting of n regular unit octagons.

Original entry on oeis.org

1, 1, 3, 11, 50, 269, 1605, 10102, 65323, 430302, 2868320, 19299334, 130807068, 892075515, 6115673262

Offset: 1

Sascha Kurz, Feb 07 2005

Matthias Koch and Sascha Kurz, Enumeration of generalized polyominoes, arXiv:math/0605144 [math.CO], 2006.
S. Kurz, k-polyominoes.

Cf. A000577, A000104, A000228, A103465, A103465, A103467, A103468.

Cf. A000577, A000104, A000228, A103465, A103467, A103468, A103469, A103470, A103471, A103472, A103473, A115071, A120102, A120103, A120104.

More terms from Sascha Kurz, Jun 09 2006

Definition corrected by John Mason and Sascha Kurz, Sep 20 2020

A103467 Number of polyominoes consisting of n regular unit 9-gons.

Original entry on oeis.org

1, 1, 3, 14, 82, 585, 4418, 34838, 280014, 2285047, 18838395, 156644526, 1311575691

Offset: 1

Sascha Kurz, Feb 07 2005

Matthias Koch and Sascha Kurz, Enumeration of generalized polyominoes, arXiv:math/0605144 [math.CO], 2006.
S. Kurz, k-polyominoes.

Cf. A000577, A000104, A000228, A103465, A103466, A103468, A103469, A103470, A103471, A103472, A103473, A115071, A120102, A120103, A120104.

More terms from Sascha Kurz, Jun 09 2006

Definition corrected by John Mason and Sascha Kurz, Sep 20 2020

A135711 Minimal perimeter of a polyhex with n cells.

Original entry on oeis.org

6, 10, 12, 14, 16, 18, 18, 20, 22, 22, 24, 24, 26, 26, 28, 28, 30, 30, 30, 32, 32, 34, 34, 34, 36, 36, 36, 38, 38, 38, 40, 40, 40, 42, 42, 42, 42, 44, 44, 44, 46, 46, 46, 46, 48, 48, 48, 48, 50, 50, 50, 50, 52, 52, 52, 52, 54, 54, 54, 54, 54, 56, 56, 56, 56, 58, 58, 58, 58, 58, 60, 60

Offset: 1

Tanya Khovanova, Mar 04 2008

nonn

Y. S. Kupitz, "On the maximal number of appearances of the minimal distance among n points in the plane", in Intuitive geometry: Proceedings of the 3rd international conference held in Szeged, Hungary, 1991; Amsterdam: North-Holland: Colloq. Math. Soc. Janos Bolyai. 63, 217-244.

Michael De Vlieger, Table of n, a(n) for n = 1..10000
Li Gan, Stéphane Ouvry, and Alexios P. Polychronakos, Algebraic area enumeration of random walks on the honeycomb lattice, arXiv:2107.10851 [math-ph], 2021.
Greg Malen, Érika Roldán, and Rosemberg Toalá-Enríquez, Extremal {p, q}-Animals, Ann. Comb. (2023). See Corollary 1.9 at p. 8.

Cf. A000228 (number of hexagonal polyominoes (or planar polyhexes) with n cells), A135708.

Analogs for triangles, squares, cubes: A067628, A027709, A075777.

Table[2Ceiling[Sqrt[12n-3]],{n,120}] (* Harvey P. Dale, Dec 29 2019 *)

It is easy to use the formula of Harborth given in A135708 to show that a(n) = 2*ceiling(sqrt(12*n-3)). - Sascha Kurz, Mar 05 2008

2*A135708(n) - a(n) = 6n. - Tanya Khovanova, Mar 07 2008

More terms from N. J. A. Sloane, Mar 05 2008

cp's OEIS Frontend

A120102 Number of polyominoes consisting of 8 regular unit n-gons.

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A120104 Number of polyominoes consisting of 10 regular unit n-gons.

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A323930 Polycyclic aromatic hydrocarbons (for precise definition see He and He, 1986).

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A005963 Number of restricted hexagonal polyominoes with n cells.

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A036359 Number of branched catafusenes with n condensed hexagons.

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A103468 Number of polyominoes consisting of n regular unit 10-gons.

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A120103 Number of polyominoes consisting of 9 regular unit n-gons.

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A103466 Number of polyominoes consisting of n regular unit octagons.

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A103467 Number of polyominoes consisting of n regular unit 9-gons.

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A135711 Minimal perimeter of a polyhex with n cells.

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