## S000804

Triangle in which the k-th term in n-th row has index of the S000803(n,k)-gonal number that equals A063778(n).

2, 3, 2, 5, 3, 2, 8, 6, 3, 2, 15, 9, 5, 3, 2, 33, 17, 11, 6, 3, 2, 49, 35, 25, 10, 7, 5, 2, 154, 55, 35, 14, 10, 7, 5, 2, 153, 77, 63, 21, 11, 9, 6, 3, 2, 105, 63, 35, 27, 18, 14, 9, 5, 3, 2, 664, 40, 38, 35, 28, 19, 14, 10, 7, 4, 2, 638, 261, 99, 71, 66, 33, 29

1

Note that each row ends with 2.

T. D. Noe, Plot of 27 rows

T. D. Noe, Table of 27 rows

Eric W. Weisstein, MathWorld: Polygonal Number

(Mma) s = {3, 6, 15, 36, 225, 561, 1225, 11935, 11781, 27405, 220780, 203841, 3368925, 4921840, 7316001, 33631521, 142629201, 879207616, 1383958576, 3800798001, 12524486976, 181285005825, 118037679760, 239764947345, 738541591425, 1289707733601, 1559439365121}; k =.; f =.; q = Table[sol = Reduce[k ((f - 2) k - (f - 4))/2 == s[[n]] && k > 0, {f, k}, Integers]; {Table[sol[[i, 1, 2]], {i, 2, Length[sol]}], Table[sol[[i, 2, 2]], {i, 2, Length[sol]}]}, {n, Length[s]}]; Transpose[q][[2]]

Cf. A063778, S000803.

nonn,tabl

T. D. Noe, Dec 17 2015