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%I #8 Dec 26 2017 23:30:13
%S 0,0,0,0,1,1,3,4,9,13,23,29,48,60,92,109,158,186,258,296,397,451,589,
%T 658,841,933,1169,1283,1582,1728,2100,2275,2732,2948,3502,3756,4419,
%U 4725,5511,5866,6789,7207,8283,8761,10006,10560,11990,12617,14250,14968
%N Number of integer-sided pentagons having perimeter n.
%C Rotations and reversals are counted only once. Note that this is different from A069906, which counts pentagons whose sides are nondecreasing.
%H James East, Ron Niles, <a href="https://arxiv.org/abs/1710.11245">Integer polygons of given perimeter</a>, arXiv:1710.11245 [math.CO], 2017.
%F Empirical g.f.: -x^5*(x^12 +2*x^9 +2*x^8 +2*x^7 +5*x^6 +3*x^5 +2*x^4 +2*x^3 +x^2 +x +1) / ((x -1)^5*(x +1)^4*(x^2 +1)^2*(x^4 +x^3 +x^2 +x +1)). - _Colin Barker_, Oct 27 2013
%e The three pentagons having perimeter 7 are (1,1,1,2,2), (1,1,2,1,2) and (1,1,1,1,3).
%t Needs["DiscreteMath`Combinatorica`"]; Table[s=Select[Partitions[n], Length[ # ]==5 && #[[1]]<Total[Rest[ # ]]&]; cnt=0; Do[cnt=cnt+Length[ListNecklaces[5,s[[i]],Dihedral]], {i,Length[s]}]; cnt, {n,50}]
%Y Cf. A057886 (quadrilaterals), A124286 (hexagons), A124287 (k-gons).
%K nonn
%O 1,7
%A _T. D. Noe_, Oct 24 2006