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A131488
a(n) is the number of polyhexes with n edges, including inner edges.
1
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
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
KEYWORD
hard,more,nonn
AUTHOR
Tanya Khovanova, Jul 28 2007
EXTENSIONS
Extended to a(48). - R. J. Mathar, Feb 23 2021
STATUS
approved