A340947 Number of ways to write n as an ordered sum of 10 squares of positive integers.

1, 0, 0, 10, 0, 0, 45, 0, 10, 120, 0, 90, 210, 0, 360, 262, 45, 840, 300, 360, 1260, 480, 1260, 1350, 1015, 2520, 1560, 2200, 3150, 2880, 4186, 2880, 5430, 6240, 3780, 8300, 7080, 7920, 11160, 7320, 13257, 14640, 10600, 16470, 18570, 18240, 19620, 22230, 25135, 27720, 28020, 28480, 38160

Offset: 10

Author

Ilya Gutkovskiy, Jan 31 2021

Keywords

• nonn

Links

• David A. Corneth, Table of n, a(n) for n = 10..10009
• Index entries for sequences related to sums of squares

Crossrefs

Cf. A000144, A000290, A010052, A025434, A045852, A063691, A063725, A063730, A340481, A340905, A340906, A340915, A340946.

Column k=10 of A337165.

Programs

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, 10):
seq(a(n), n=10..62);  # Alois P. Heinz, Jan 31 2021

Mathematica

nmax = 62; CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^10/1024, {x, 0, nmax}], x] // Drop[#, 10] &

Formula

G.f.: (theta_3(x) - 1)^10 / 1024, where theta_3() is the Jacobi theta function.