A124286 Number of integer-sided hexagons having perimeter n.

0, 0, 0, 0, 0, 1, 1, 4, 7, 15, 25, 46, 72, 113, 172, 248, 360, 491, 686, 896, 1217, 1536, 2031, 2504, 3236, 3905, 4955, 5880, 7336, 8586, 10556, 12208, 14823, 16964, 20364, 23106, 27456, 30906, 36399, 40692, 47532, 52816, 61237, 67672, 77941, 85701

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 A069907, which counts hexagons whose sides are nondecreasing.

Examples

			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).
		

Links

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

Crossrefs

Cf. A057886 (quadrilaterals), A124285 (pentagons), A124287 (k-gons).

Programs

Mathematica

Needs["DiscreteMath`Combinatorica`"]; Table[s=Select[Partitions[n], Length[ # ]==6 && #[[1]]
				

Formula

Empirical g.f.: x^6*(x^13 +3*x^12 +6*x^11 +6*x^10 +10*x^9 +9*x^8 +12*x^7 +10*x^6 +8*x^5 +5*x^4 +4*x^3 +2*x^2 +x +1) / ((x -1)^6*(x +1)^5*(x^2 -x +1)*(x^2 +1)^2*(x^2 +x +1)^2). - Colin Barker, Oct 27 2013