A115289 a(n) is the smallest number representable in exactly n ways as a sum of one triangular number and 2 squares (each of them >= 0).

0, 1, 5, 10, 19, 26, 55, 46, 53, 116, 86, 128, 173, 145, 200, 170, 221, 235, 236, 305, 341, 326, 491, 425, 548, 431, 676, 530, 536, 635, 656, 851, 905, 695, 1118, 950, 1040, 1171, 1241, 1031, 1076, 1115, 1325, 1661, 1943, 1391, 1531, 1691, 1790, 1670, 2291, 2081

Offset: 1

Author

Giovanni Resta, Jan 19 2006

Keywords

• nonn

Examples

			a(4)=10 since 10 can be expressed in 4 ways,
10=T(4)+0^2+0^2 = T(3)+0^2+2^2 = T(1)+0^2+3^2 = T(0)+1^2+3^2 and none of the numbers from 0 to 9 can be expressed in 4 ways.
		

Crossrefs

Cf. A115288, A000437, A061262.

Programs

Mathematica

V = Table[0, {i, 5000}]; T[n]:=n(n+1)/2; Do[a = T[i]+j^2+k^2; If[a<5000, V[[a+1]]++ ], {i, 0, 100}, {j, 0, 71}, {k, 0, j}]; Table[Position[V, z][[1, 1]]-1, {z, 60}]