A340481 Number of ways to write n as an ordered sum of 5 squares of positive integers.

1, 0, 0, 5, 0, 0, 10, 0, 5, 10, 0, 20, 5, 0, 30, 6, 10, 20, 20, 30, 5, 30, 30, 20, 35, 10, 60, 45, 0, 60, 50, 30, 45, 50, 60, 70, 35, 30, 110, 50, 31, 110, 80, 80, 50, 70, 120, 70, 75, 90, 140, 110, 20, 140, 160, 60, 135, 120, 120, 180, 40, 130, 230, 80, 120, 170, 200, 155, 85, 200, 190

Offset

5,4

Links

Alois P. Heinz, Table of n, a(n) for n = 5..20000

Index entries for sequences related to sums of squares

Formula

G.f.: (theta_3(x) - 1)^5 / 32, 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, 5):
seq(a(n), n=5..75);  # Alois P. Heinz, Jan 31 2021

Mathematica

nmax = 75; CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^5/32, {x, 0, nmax}], x] // Drop[#, 5] &

Crossrefs

Cf. A000132, A000290, A010052, A025429, A038671, A063691, A063725, A063730, A340905, A340906, A340915, A340946, A340947.

Column k=5 of A337165.

Sequence in context: A068459 A099222 A341796 * A236232 A019178 A263913

Adjacent sequences: A340478 A340479 A340480 * A340482 A340483 A340484

Keyword

nonn,look

Author

Ilya Gutkovskiy, Jan 31 2021

Status

approved