A330861 Number of ways to represent n as a sum of 2 triangular numbers and a perfect square.

1, 2, 2, 2, 3, 2, 3, 4, 2, 2, 5, 4, 3, 4, 2, 4, 6, 4, 3, 4, 5, 4, 7, 2, 3, 8, 4, 4, 5, 6, 4, 8, 6, 2, 5, 4, 6, 8, 7, 4, 8, 4, 5, 8, 2, 6, 10, 8, 3, 6, 6, 6, 10, 4, 4, 10, 8, 6, 7, 6, 7, 8, 6, 2, 9, 10, 6, 12, 4, 4, 11, 8, 6, 10, 8, 4, 10, 6, 5, 6, 10, 10, 12, 6, 5, 14, 4, 8, 9, 4, 6, 12

Offset

0,2

Comments

The range of the two triangular numbers and the square is the nonnegative numbers.

Links

Table of n, a(n) for n=0..91.

Example

a(0)=1 because there is one representation 0 = T(0)+T(0)+0^2.
a(1)=2 because there are 2 representations 1 = T(0)+T(0)+1^2 = T(0)+T(1)+0^2.
a(4)=3 because there are 3 representations 4 = T(0)+T(0)+2^2 = T(0)+T(2)+1^2 = T(1)+T(2)+0^2.

Maple

A330861 := proc(n)
    local a, t1idx, t2idx, t1, t2;
    a := 0 ;
    for t1idx from 0 do
        t1 := A000217(t1idx) ;
        if t1 > n then
            break;
        end if;
        for t2idx from t1idx do
            t2 := A000217(t2idx) ;
            if t1+t2 > n then
                break;
            end if;
            if issqr(n-t1-t2) then
                a := a+1 ;
            end if;
        end do:
    end do:
    a ;
end proc:

Crossrefs

Cf. A115288 (greedy inverse).

Sequence in context: A128435 A369219 A220415 * A286565 A219354 A026903

Adjacent sequences: A330858 A330859 A330860 * A330862 A330863 A330864

Keyword

nonn

Author

R. J. Mathar, Apr 28 2020

Status

approved