A265134 Numbers that are the sum of two distinct nonzero triangular numbers in exactly two ways.

16, 31, 46, 51, 76, 94, 111, 121, 123, 126, 133, 141, 146, 156, 157, 172, 174, 186, 191, 196, 198, 216, 225, 226, 231, 237, 241, 246, 259, 268, 281, 286, 289, 291, 297, 301, 310, 315, 321, 326, 328, 336, 346, 354, 366, 367, 379, 384, 391, 396, 412, 416

Offset: 1

Author

Arkadiusz Wesolowski, Dec 02 2015

Keywords

• nonn

Crossrefs

Cf. A000217, A051533, A260647, A265140 (exactly one way), A262749 (more than one way), A265135 (more than two ways), A265136 (exactly three ways), A265137 (more than three ways), A265138 (exactly four ways).

Programs

Mathematica

r = 416; lst = Table[0, {r}]; lim = Floor[Sqrt[8*r - 7]]; Do[num = (i^2 + i)/2 + (j^2 + j)/2; If[num <= r, lst[[num]]++], {i, lim}, {j, i - 1}]; Flatten@Position[lst, 2]
Module[{nn=40,trnos},trnos=Accumulate[Range[nn]];Select[PositionIndex[ Sort[ Counts[Total/@Subsets[trnos,{2}]]]][2],#<=Last[trnos]&]] (* The program uses the PositionIndex and Counts functions from Mathematica version 10 *) (* Harvey P. Dale, Dec 25 2015 *)