A341401 Number of nonnegative solutions to (x_1)^2 + (x_2)^2 + ... + (x_6)^2 <= n.

1, 7, 22, 42, 63, 99, 160, 220, 265, 337, 457, 577, 672, 792, 978, 1178, 1319, 1469, 1739, 2039, 2255, 2507, 2882, 3242, 3513, 3819, 4269, 4769, 5159, 5555, 6181, 6841, 7246, 7666, 8401, 9181, 9763, 10363, 11188, 12108, 12828, 13434, 14394, 15534, 16359, 17211, 18477, 19677

Offset: 0

Author

Ilya Gutkovskiy, Feb 10 2021

Keywords

• nonn

Comments

Partial sums of A045848.

Links

• Index entries for sequences related to sums of squares

Crossrefs

Cf. A000122, A000606, A003059, A045848, A055405, A055412, A175361, A224212, A224213, A302862, A341400, A341402.

Programs

Maple

b:= proc(n, k) option remember; `if`(n=0, 1, `if`(n<0 or k<1, 0,
      b(n, k-1)+add(b(n-j^2, k-1), j=1..isqrt(n))))
    end:
a:= proc(n) option remember; b(n, 6)+`if`(n>0, a(n-1), 0) end:
seq(a(n), n=0..47);  # Alois P. Heinz, Feb 10 2021

Mathematica

nmax = 47; CoefficientList[Series[(1 + EllipticTheta[3, 0, x])^6/(64 (1 - x)), {x, 0, nmax}], x]

Formula

G.f.: (1 + theta_3(x))^6 / (64 * (1 - x)).

a(n^2) = A055405(n).