A234004 Smallest number which is the sum of two positive triangular numbers (A000217) in at least n ways.
2, 16, 81, 471, 1056, 1381, 6906, 6906, 17956, 34531, 40056, 40056, 200281, 200281, 200281, 200281, 520731, 520731, 1001406, 1001406, 1482081, 1482081, 1482081, 1482081, 7410406, 7410406, 7410406, 7410406, 7410406, 7410406, 7410406, 7410406
Offset: 1
Keywords
Examples
2 = 1+1; 16 = 1+15 = 6+10; 81 = 3+78 = 15+66 = 36+45.
Links
- Donovan Johnson, Table of n, a(n) for n = 1..216
Programs
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Mathematica
poly[n_,k_]:=n (n-1)(k-2)/2+n;nn=10^5;order=3;t2=Table[0,{nn}];n2=Floor[(-4+#+Sqrt[(-4+#)^2+8 (-2+#) nn])/(2 (-2+#))&[order]];Do[r=Plus@@poly[{a,b},order];If[r<=nn,t2[[r]]++],{a,n2},{b,a,n2}];t={};n=1;While[a=Position[t2,?(#>=n&),1,1];a!={},AppendTo[t,a[[1,1]]];n++];t (* after _T. D. Noe (A048610) *)