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%I
%S 0,0,0,0,0,1,1,4,7,15,25,46,72,113,172,248,360,491,686,896,1217,1536,
%T 2031,2504,3236,3905,4955,5880,7336,8586,10556,12208,14823,16964,
%U 20364,23106,27456,30906,36399,40692,47532,52816,61237,67672,77941,85701
%N Number of integer-sided hexagons having perimeter n.
%C Rotations and reversals are counted only once. Note that this is different from A069907, which counts hexagons whose sides are nondecreasing.
%e The four hexagons having perimeter 8 are (1,1,1,1,2,2), (1,1,1,2,1,2), (1,1,2,1,1,2) and (1,1,1,1,1,3).
%t Needs["DiscreteMath`Combinatorica`"]; Table[s=Select[Partitions[n], Length[ # ]==6 && #[[1]]<Total[Rest[ # ]]&]; cnt=0; Do[cnt=cnt+Length[ListNecklaces[6,s[[i]],Dihedral]], {i,Length[s]}]; cnt, {n,50}]
%Y Cf. A057886 (quadrilaterals), A124285 (pentagons), A124287 (k-gons).
%K nonn
%O 1,8
%A _T. D. Noe_, Oct 24 2006
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