A131487 a(n) is the number of polyominoes with n edges, including inner edges.
0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 1, 4, 0, 1, 11, 1, 7, 27, 4, 21, 85, 21, 92, 264, 89, 345, 914, 394, 1405, 3155, 1736, 5530, 11400, 7586, 22022, 41756, 32702, 87158, 156412, 139253, 346836, 592661, 589101, 1379837, 2275935, 2476770, 5501846, 8830267, 10363627, 21970992, 34594887, 43188260, 87950618
Offset: 1
Examples
A single cell has 4 edges; a domino has 7 edges (this includes the edge between the two cells); both trominoes have 10 edges; their possible orientations are not considered distinct. Thus a(4) = a(7) = 1, a(10) = 2, and a(n) = 0 for n < 10 not equal to 4 or 7. a(22) = 85 = 83 + 2: there are 83 polyominoes with 7 cells and perimeter 16 (such as a 1 X 7 strip) and two polyominoes with 8 cells and perimeter 12 (a 3 X 3 square without a corner and a 4 X 2 rectangle), and each of these polyominoes has 22 edges. a(23) = 21. a(24) = 91+1. a(25) = 255+9. a(26) = 89. a(27) = 339+6. a(28) = 847+67. a(34) = 9734+1655+11. a(35) = 7412+174. - _R. J. Mathar_, Feb 22 2021
Links
- Andrew Clarke, Isoperimetrical Polyominoes
Crossrefs
Formula
See A342243 for formula.
Extensions
a(23)-a(35) from R. J. Mathar, Feb 22 2021
a(36)-a(39) from R. J. Mathar, Mar 11 2021
a(40)-a(44) from R. J. Mathar, Mar 24 2021
a(45)-a(54) from John Mason, Apr 28 2023
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