A131488 a(n) is the number of polyhexes with n edges, including inner edges.

0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 1, 5, 0, 1, 3, 6, 12, 3, 4, 14, 26, 39, 10, 25, 70, 116, 139, 67, 152, 347, 514, 567, 414, 884, 1744, 2408, 2561, 2498, 4967

Offset

1,16

Comments

An n-celled polyhex with perimeter p has (6n+p)/2 edges. The maximum number of edges in an n-celled polyhex is 5n+1.

Given Clarke's table T(p,n), a(n) is an antidiagonal sum selecting entries in a (1,3)-leaper's moves. - R. J. Mathar, Feb 23 2021

Links

Table of n, a(n) for n=1..48.

Andrew Clarke, Isoperimetrical Polyhexes

Example

a(31) = T(p=26,A=6) + T(p=20,A=7) = 36+3 = 39. a(34) = T(p=26,A=7) + T(p=20,A=8) = 69+1 = 70. a(35) = 107+9. a(36) = 118+21. a(41) = 411+155+1. a(44) = 1621 +123. a(45) = 1986+420+2. a(46) = 1489+1046+26. - R. J. Mathar, Feb 23 2021

Crossrefs

Cf. A000228: Number of hexagonal polyominoes (or planar polyhexes) with n cells. A057779: Hexagonal polyominoes (or polyhexes, A000228) with perimeter 2n. A038142: Number of planar cata-polyhexes with n cells. A131487: analog for square tiling.

Sequence in context: A035671 A190164 A253938 * A333361 A363665 A308183

Adjacent sequences: A131485 A131486 A131487 * A131489 A131490 A131491

Keyword

hard,more,nonn

Author

Tanya Khovanova, Jul 28 2007

Extensions

Extended to a(48). - R. J. Mathar, Feb 23 2021

Status

approved