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A265135
Numbers that are the sum of two distinct nonzero triangular numbers in more than two ways.
7
81, 106, 181, 211, 256, 276, 331, 361, 381, 406, 456, 471, 531, 556, 601, 606, 616, 631, 666, 681, 706, 718, 731, 781, 786, 856, 861, 871, 906, 931, 939, 956, 981, 991, 1051, 1056, 1126, 1131, 1156, 1186, 1206, 1231, 1281, 1296, 1341, 1381, 1446, 1456
OFFSET
1,1
MATHEMATICA
r = 1456; 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, n_ /; n > 2]
Module[{nn=60, trnos}, trnos=Accumulate[Range[nn]]; Select[Sort[Flatten[ Table[ PositionIndex[Counts[Total/@Subsets[trnos, {2}]]][i], {i, 3, nn}]]], #<= Last[trnos]&]] (* The program uses the PositionIndex and Counts functions from Mathematica version 10 *) (* Harvey P. Dale, Dec 26 2015 *)
CROSSREFS
Cf. A000217, A051533, A260647, A265140 (exactly one way), A262749 (more than one way), A265134 (exactly two ways), A265136 (exactly three ways), A265137 (more than three ways), A265138 (exactly four ways).
Sequence in context: A202002 A249613 A064828 * A265136 A120457 A129151
KEYWORD
nonn
AUTHOR
STATUS
approved