A341402 Number of nonnegative solutions to (x_1)^2 + (x_2)^2 + ... + (x_7)^2 <= n.

1, 8, 29, 64, 106, 169, 281, 422, 548, 702, 961, 1276, 1556, 1864, 2326, 2893, 3390, 3852, 4545, 5455, 6253, 7002, 8080, 9361, 10453, 11496, 12903, 14618, 16194, 17643, 19589, 22011, 24027, 25714, 28143, 31188, 33792, 36137, 39203, 42920, 46294, 49108, 52580, 57165, 61365

Offset

0,2

Comments

Partial sums of A045849.

Links

Table of n, a(n) for n=0..44.

Index entries for sequences related to sums of squares

Formula

G.f.: (1 + theta_3(x))^7 / (128 * (1 - x)).

a(n^2) = A055406(n).

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, 7)+`if`(n>0, a(n-1), 0) end:
seq(a(n), n=0..44);  # Alois P. Heinz, Feb 10 2021

Mathematica

nmax = 44; CoefficientList[Series[(1 + EllipticTheta[3, 0, x])^7/(128 (1 - x)), {x, 0, nmax}], x]

Crossrefs

Cf. A000122, A000606, A003059, A045849, A055406, A055413, A224212, A224213, A302862, A341400, A341401.

Sequence in context: A299678 A300310 A171442 * A247541 A320695 A093809

Adjacent sequences: A341399 A341400 A341401 * A341403 A341404 A341405

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 10 2021

Status

approved