A038671 Number of nonnegative solutions of x1^2 + x2^2 + ... + x5^2 = n.

1, 5, 10, 10, 10, 21, 30, 20, 15, 35, 50, 40, 30, 45, 70, 60, 30, 55, 100, 80, 56, 90, 110, 80, 60, 90, 140, 130, 80, 115, 190, 140, 55, 120, 200, 170, 130, 145, 200, 200, 120, 145, 270, 220, 140, 231, 290, 200, 110

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to sums of squares

Programs

Mathematica

(1 + EllipticTheta[3, 0, q])^5/32 + O[q]^50 // CoefficientList[#, q]& (* Jean-François Alcover, Aug 26 2019 *)

PARI

seq(n)=Vec((sum(k=0, sqrtint(n), x^(k^2)) + O(x*x^n))^5) \\ Andrew Howroyd, Aug 08 2018

Formula

Coefficient of q^n in (1 + q + q^4 + q^9 + q^16 + q^25 + q^36 + q^49 + q^64 + ...)^5.

G.f.: (1 + theta_3(q))^5/32, where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Aug 08 2018