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A265137
Numbers that are the sum of two distinct nonzero triangular numbers in more than three ways.
7
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.
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
KEYWORD
nonn
AUTHOR
STATUS
approved