This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A265136 #14 Dec 25 2015 12:43:00
%S A265136 81,106,181,211,256,276,331,361,381,406,456,556,606,631,666,681,706,
%T A265136 718,731,781,856,861,931,939,956,981,1051,1131,1206,1231,1456,1506,
%U A265136 1563,1606,1631,1681,1731,1732,1756,1831,1891,1901,1956,1981,2081,2095,2101
%N A265136 Numbers that are the sum of two distinct nonzero triangular numbers in exactly three ways.
%t A265136 r = 2101; 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, 3]
%t A265136 Module[{nn=70,trnos},trnos=Accumulate[Range[nn]];Select[ PositionIndex[ Sort[ Counts[Total/@Subsets[trnos,{2}]]]][3],#<=Last[trnos]&]] (* The program uses the PositionIndex and Counts functions from Mathematica version 10 *) (* _Harvey P. Dale_, Dec 25 2015 *)
%Y A265136 Cf. A000217, A051533, A260647, A265140 (exactly one way), A262749 (more than one way), A265134 (exactly two ways), A265135 (more than two ways), A265137 (more than three ways), A265138 (exactly four ways).
%K A265136 nonn
%O A265136 1,1
%A A265136 _Arkadiusz Wesolowski_, Dec 02 2015