|
%I #14 Dec 25 2015 12:43:00
%S 81,106,181,211,256,276,331,361,381,406,456,556,606,631,666,681,706,
%T 718,731,781,856,861,931,939,956,981,1051,1131,1206,1231,1456,1506,
%U 1563,1606,1631,1681,1731,1732,1756,1831,1891,1901,1956,1981,2081,2095,2101
%N Numbers that are the sum of two distinct nonzero triangular numbers in exactly three ways.
%t 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 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 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 nonn
%O 1,1
%A _Arkadiusz Wesolowski_, Dec 02 2015
|
