A340905 Number of ways to write n as an ordered sum of 6 squares of positive integers.

1, 0, 0, 6, 0, 0, 15, 0, 6, 20, 0, 30, 15, 0, 60, 12, 15, 60, 31, 60, 30, 60, 90, 36, 86, 60, 120, 120, 15, 180, 141, 60, 165, 140, 180, 186, 120, 180, 285, 156, 126, 360, 255, 216, 270, 260, 390, 240, 262, 420, 426, 360, 210, 540, 530, 216, 540, 540, 480, 600, 300, 600, 825, 312, 576, 840

Offset

6,4

Links

Alois P. Heinz, Table of n, a(n) for n = 6..20000

Index entries for sequences related to sums of squares

Formula

G.f.: (theta_3(x) - 1)^6 / 64, 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, 6):
seq(a(n), n=6..71);  # Alois P. Heinz, Jan 31 2021

Mathematica

nmax = 71; CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^6/64, {x, 0, nmax}], x] // Drop[#, 6] &

Crossrefs

Cf. A000141, A000290, A010052, A025430, A045848, A063691, A063725, A063730, A340481, A340906, A340915, A340946, A340947.

Column k=6 of A337165.

Sequence in context: A243254 A263850 A341797 * A210446 A002044 A230968

Adjacent sequences: A340902 A340903 A340904 * A340906 A340907 A340908

Keyword

nonn,look

Author

Ilya Gutkovskiy, Jan 31 2021

Status

approved