A265137 Numbers that are the sum of two distinct nonzero triangular numbers in more than three ways.

471, 531, 601, 616, 786, 871, 906, 991, 1056, 1126, 1156, 1186, 1281, 1296, 1341, 1381, 1446, 1486, 1551, 1576, 1602, 1641, 1656, 1771, 1806, 1836, 1896, 1906, 1921, 2031, 2044, 2061, 2146, 2226, 2265, 2281, 2316, 2356, 2401, 2421, 2451, 2486, 2551, 2646

Offset

1,1

Comments

If there exists any 3 X 3 magic square composed of triangular numbers, then its magic sum is a(n) + A000217(m) for some m and n.

Links

Table of n, a(n) for n=1..44.

Mathematica

r = 2646; 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 > 3]
Module[{nn=80, trnos}, trnos=Accumulate[Range[nn]]; Select[Sort[ Flatten[ Table[ PositionIndex[Counts[Total/@Subsets[trnos, {2}]]][i], {i, 4, 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), A265135 (more than two ways), A265136 (exactly three ways), A265138 (exactly four ways).

Sequence in context: A251152 A345535 A345787 * A265138 A269749 A138132

Adjacent sequences: A265134 A265135 A265136 * A265138 A265139 A265140

Keyword

nonn

Author

Arkadiusz Wesolowski, Dec 02 2015

Status

approved