A115288 a(n) is the smallest number representable in exactly n ways as a sum of 2 triangular numbers and one square (each of them >= 0).

0, 1, 4, 7, 10, 16, 22, 25, 64, 46, 70, 67, 92, 85, 160, 115, 106, 136, 200, 157, 190, 172, 256, 235, 568, 277, 370, 337, 400, 367, 340, 550, 556, 442, 1102, 445, 472, 631, 610, 535, 682, 697, 652, 1075, 956, 850, 1984, 865, 1172, 997, 862, 1081, 1462, 1135, 1060

Offset: 1

Author

Giovanni Resta, Jan 19 2006

Keywords

• nonn

Examples

			a(4)=7 since 7 can be expressed in 4 ways, 7= T(3)+T(1)+0^2 = T(3)+T(0)+1^2 = T(2)+T(0)+2^2 = T(2)+T(2)+1^2 and none of the numbers from 0 to 6 can be expressed in 4 ways.
		

Crossrefs

Cf. A115289, A000437, A061262, A330861.

Programs

Maple

a := [seq(0,n=0..100)] ;
for k from 0 do
    a330861 := A330861(k) ;
    if a330861 <= nops(a) then
        if op(a330861,a) = 0 then
            a := subsop(a330861=k,a) ;
            print(a) ;
        end if;
    end if;
    if not member(0,[op(2..nops(a),a)]) then
        break;
    end if;
end do: # R. J. Mathar, Apr 28 2020

Mathematica

V=Table[0, {i, 2500}]; T[n]:=n(n+1)/2; Do[a=T[i]+T[j]+k^2;If[a<2500, V[[a+1]]++ ], {i, 0, 71}, {j, 0, i}, {k, 0, 50}]; Table[Position[V, z][[1, 1]]-1, {z, 60}]