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 A124286 Number of integer-sided hexagons having perimeter n. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS Rotations and reversals are counted only once. Note that this is different from A069907, which counts hexagons 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^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 EXAMPLE 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). MATHEMATICA Needs["DiscreteMath`Combinatorica`"]; Table[s=Select[Partitions[n], Length[ # ]==6 && #[[1]]

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Last modified June 24 14:24 EDT 2021. Contains 345417 sequences. (Running on oeis4.)