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%I #17 Feb 24 2021 02:33:37
%S 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,
%T 25,70,116,139,67,152,347,514,567,414,884,1744,2408,2561,2498,4967
%N a(n) is the number of polyhexes with n edges, including inner edges.
%C 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.
%C 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
%H Andrew Clarke, <a href="http://www.recmath.com/PolyPages/PolyPages/IsopolyH.htm">Isoperimetrical Polyhexes</a>
%e 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
%Y 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.
%K hard,more,nonn
%O 1,16
%A _Tanya Khovanova_, Jul 28 2007
%E Extended to a(48). - _R. J. Mathar_, Feb 23 2021
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