A002841
Number of 3-connected self-dual planar graphs with 2n edges.
Original entry on oeis.org
1, 1, 2, 6, 16, 50, 165, 554, 1908, 6667, 23556, 84048, 302404, 1095536, 3993623
Offset: 3
- 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).
- C. J. Bouwkamp & N. J. A. Sloane, Correspondence, 1971
- M. B. Dillencourt, Polyhedra of small orders and their Hamiltonian properties, Journal of Combinatorial Theory, Series B, Volume 66, Issue 1, January 1996, Pages 87-122. See bottom of Table IV on page 98.
- P. J. Federico, Enumeration of polyhedra: the number of 9-hedra, J. Combin. Theory, 7 (1969), 155-161.
- House of Graphs, Planar graphs
- Eric Weisstein's World of Mathematics, Self-Dual Graph
A006759
Number of one-sided strictly 3-dimensional polyominoes with n cells.
Original entry on oeis.org
0, 0, 0, 3, 17, 131, 915, 6553, 47026, 341888, 2505449, 18534827, 138224058, 1038594326, 7856087894, 59782042225, 457359506070, 3515816578512, 27143401299351, 210372490707568
Offset: 1
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
-
A[s_Integer] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[ Import["https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {, }][[All, 2]]];
A000105 = A@000105;
A000162 = A@000162;
a[n_] := A000162[[n]] - A000105[[n + 1]];
a /@ Range[16] (* Jean-François Alcover, Jan 16 2020 *)
A038172
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.
Original entry on oeis.org
1, 1, 5, 28, 225, 2274, 24955, 286143, 3367443, 40358811, 490598186
Offset: 1
This extends earlier work of Torsten Sillke (TORSTEN.SILLKE(AT)LHSYSTEMS.COM). Added the 10th term.
A038180
Number of "connected animals" formed from n square- or hexagon-connected truncated octahedra in the b.c.c. lattice, allowing translation and rotations of the lattice.
Original entry on oeis.org
1, 2, 6, 44, 394, 4680, 59361, 789303, 10742595, 148921162, 2093400002, 29769338104
Offset: 1
Torsten Sillke (TORSTEN.SILLKE(AT)LHSYSTEMS.COM)
A270862
Number of polycubes with n cells, allowing edge connections as well as face connections, distinguishing mirror images.
Original entry on oeis.org
1, 2, 9, 88, 1103, 17570, 295506, 5168034, 92436673
Offset: 1
a(3)=9 because there are 8 ways to join 3 cells in the cubic grid at faces or edges, identifying reflections, and one of those 8 has distinct mirror images, which makes 9.
- Jørgen Lou, Danish Patent 126840 (27 August 1973).
A292065
Number of Besźel [Beszel] Polycubes with n cells, distinguishing mirror images. A Besźel polycube is a polycube whose cells each have two or more even coordinates.
Original entry on oeis.org
1, 1, 2, 4, 12, 27, 106, 339, 1336, 5029
Offset: 1
a(4) = 4 because 4 of the 8 tetracubes (I, L, T, K) can be embedded in the Besźel section of the cubic grid.
- China Miéville, The City & the City, Macmillan, 2009.
Cf.
A292157: Number of Besźel Polycubes with n cells, identifying mirror images;
A000162: Number of polycubes with n cells [distinguishing mirror images].
A355966
Number of 3-dimensional polyominoes (or polycubes) with n cells that have cavities (inclusions of empty space).
Original entry on oeis.org
20, 404, 6164, 75917, 835491
Offset: 11
Cf.
A357083 (without distinguished reflections).
A376964
Number of polycubes of size n and symmetry class I (no symmetry).
Original entry on oeis.org
0, 0, 0, 0, 4, 46, 394, 3025, 22707, 167732, 1241417, 9221624, 68936674, 518574100, 3925132946, 29878869619, 228629549175, 1757697391087, 13570818452472, 105182527335313, 818093680980786, 6383353461322488
Offset: 1
A376965
Number of polycubes of size n and symmetry class A.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 22, 14, 31, 41, 213, 182, 321, 453, 1796
Offset: 1
A376966
Number of polycubes of size n and symmetry class B.
Original entry on oeis.org
0, 0, 0, 0, 0, 3, 4, 37, 52, 342, 502, 2836, 4343, 22622, 35405, 176176, 281141, 1363112, 2205171, 10527712, 17221126, 81462884, 134424679, 632308448
Offset: 1
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