A265138 Numbers that are the sum of two distinct nonzero triangular numbers in exactly four ways.

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

Links

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

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

Adjacent sequences: A265135 A265136 A265137 * A265139 A265140 A265141

Keyword

nonn

Author

Arkadiusz Wesolowski, Dec 02 2015

Status

approved