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

Author

Vladimir Shevelev and Peter J. C. Moses, Dec 18 2013

Keywords

• nonn

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

Crossrefs

Cf. A000217, A048610, A199809, A052346, A053587.

Programs

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) *)