

A131487


a(n) is the number of polyominoes with n edges, including inner edges.


3



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,10


COMMENTS

An ncelled polyomino with perimeter p has (4n+p)/2 edges. The maximum number of edges in an ncelled polyomino is 3n+1.


LINKS



FORMULA



EXAMPLE

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


CROSSREFS

Cf. A131482 (number of ncelled polyominoes with perimeter 2n+2), A131488 (analog for hexagonal tiling).


KEYWORD

hard,nonn


AUTHOR



EXTENSIONS



STATUS

approved



