A340946 Number of ways to write n as an ordered sum of 9 squares of positive integers.

1, 0, 0, 9, 0, 0, 36, 0, 9, 84, 0, 72, 126, 0, 252, 135, 36, 504, 156, 252, 630, 288, 756, 576, 606, 1260, 756, 1207, 1260, 1584, 2052, 1008, 2727, 2688, 1764, 3663, 2718, 3816, 4608, 2853, 5418, 6048, 4620, 5868, 7506, 7464, 7308, 8442, 8958, 11088, 10404, 9684, 13986, 14184, 13020

Offset

9,4

Links

Alois P. Heinz, Table of n, a(n) for n = 9..20000

Index entries for sequences related to sums of squares

Formula

G.f.: (theta_3(x) - 1)^9 / 512, where theta_3() is the Jacobi theta function.

Maple

b:= proc(n, t) option remember;
      `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->
      `if`(s>n, 0, b(n-s, t-1)))(j^2), j=1..isqrt(n))))
    end:
a:= n-> b(n, 9):
seq(a(n), n=9..63);  # Alois P. Heinz, Jan 31 2021

Mathematica

nmax = 63; CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^9/512, {x, 0, nmax}], x] // Drop[#, 9] &

Crossrefs

Cf. A000290, A008452, A010052, A025433, A045851, A063691, A063725, A063730, A340481, A340905, A340906, A340915, A340947.

Column k=9 of A337165.

Sequence in context: A050453 A338017 A341808 * A255292 A103636 A278006

Adjacent sequences: A340943 A340944 A340945 * A340947 A340948 A340949

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 31 2021

Status

approved