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A265134
Numbers that are the sum of two distinct nonzero triangular numbers in exactly two ways.
10
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
1,1
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 *)
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).
Sequence in context: A185980 A064816 A262749 * A220000 A132299 A240053
KEYWORD
nonn
AUTHOR
STATUS
approved