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A265134 Numbers that are the sum of two distinct nonzero triangular numbers in exactly two ways. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..52.

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

Adjacent sequences:  A265131 A265132 A265133 * A265135 A265136 A265137

KEYWORD

nonn

AUTHOR

Arkadiusz Wesolowski, Dec 02 2015

STATUS

approved

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Last modified October 21 16:04 EDT 2019. Contains 328301 sequences. (Running on oeis4.)