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 A265138 #10 Dec 25 2015 12:50:42
%S A265138 471,531,601,616,786,871,906,991,1056,1126,1156,1186,1281,1296,1341,
%T A265138 1446,1486,1551,1576,1602,1641,1656,1771,1806,1836,1896,1906,1921,
%U A265138 2044,2061,2146,2226,2265,2281,2316,2401,2421,2451,2486,2551,2646,2716,2746,2781
%N A265138 Numbers that are the sum of two distinct nonzero triangular numbers in exactly four ways.
%t A265138 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]
%t A265138 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 *)
%Y A265138 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).
%K A265138 nonn
%O A265138 1,1
%A A265138 _Arkadiusz Wesolowski_, Dec 02 2015