A265135 Numbers that are the sum of two distinct nonzero triangular numbers in more than two ways.

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

Links

Table of n, a(n) for n=1..48.

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

Adjacent sequences: A265132 A265133 A265134 * A265136 A265137 A265138

Keyword

nonn

Author

Arkadiusz Wesolowski, Dec 02 2015

Status

approved