A124285 Number of integer-sided pentagons having perimeter n.

0, 0, 0, 0, 1, 1, 3, 4, 9, 13, 23, 29, 48, 60, 92, 109, 158, 186, 258, 296, 397, 451, 589, 658, 841, 933, 1169, 1283, 1582, 1728, 2100, 2275, 2732, 2948, 3502, 3756, 4419, 4725, 5511, 5866, 6789, 7207, 8283, 8761, 10006, 10560, 11990, 12617, 14250, 14968

Offset: 1

Author

T. D. Noe, Oct 24 2006

Keywords

• nonn

Comments

Rotations and reversals are counted only once. Note that this is different from A069906, which counts pentagons whose sides are nondecreasing.

Examples

			The three pentagons having perimeter 7 are (1,1,1,2,2), (1,1,2,1,2) and (1,1,1,1,3).
		

Links

• James East, Ron Niles, Integer polygons of given perimeter, arXiv:1710.11245 [math.CO], 2017.

Crossrefs

Cf. A057886 (quadrilaterals), A124286 (hexagons), A124287 (k-gons).

Programs

Mathematica

Needs["DiscreteMath`Combinatorica`"]; Table[s=Select[Partitions[n], Length[ # ]==5 && #[[1]]
				

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