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A265138
Numbers that are the sum of two distinct nonzero triangular numbers in exactly four ways.
8
471, 531, 601, 616, 786, 871, 906, 991, 1056, 1126, 1156, 1186, 1281, 1296, 1341, 1446, 1486, 1551, 1576, 1602, 1641, 1656, 1771, 1806, 1836, 1896, 1906, 1921, 2044, 2061, 2146, 2226, 2265, 2281, 2316, 2401, 2421, 2451, 2486, 2551, 2646, 2716, 2746, 2781
OFFSET
1,1
MATHEMATICA
r = 2781; 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, 4]
Module[{nn=80, trnos}, trnos=Accumulate[Range[nn]]; Select[PositionIndex[ Sort[ Counts[Total/@Subsets[trnos, {2}]]]][4], #<=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), A265134 (exactly two ways), A265135 (more than two ways), A265136 (exactly three ways), A265137 (more than three ways).
Sequence in context: A345535 A345787 A265137 * A269749 A138132 A034284
KEYWORD
nonn
AUTHOR
STATUS
approved