OFFSET
1,7
COMMENTS
Rotations and reversals are counted only once. Note that this is different from A069906, which counts pentagons whose sides are nondecreasing.
LINKS
James East, Ron Niles, Integer polygons of given perimeter, arXiv:1710.11245 [math.CO], 2017.
FORMULA
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
EXAMPLE
The three pentagons having perimeter 7 are (1,1,1,2,2), (1,1,2,1,2) and (1,1,1,1,3).
MATHEMATICA
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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Oct 24 2006
STATUS
approved