A045848 Number of nonnegative solutions of x1^2 + x2^2 + ... + x6^2 = n.

1, 6, 15, 20, 21, 36, 61, 60, 45, 72, 120, 120, 95, 120, 186, 200, 141, 150, 270, 300, 216, 252, 375, 360, 271, 306, 450, 500, 390, 396, 626, 660, 405, 420, 735, 780, 582, 600, 825, 920, 720, 606, 960, 1140, 825

Offset

0,2

Links

T. D. Noe, Table of n, a(n) for n = 0..10000

Index entries for sequences related to sums of squares

Formula

Coefficient of q^n in (1 + q + q^4 + q^9 + q^16 + q^25 + q^36 + q^49 + q^64 + ...)^6.

G.f.: (1 + theta_3(q))^6/64, where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Aug 08 2018

Mathematica

(1 + EllipticTheta[3, 0, q])^6/64 + O[q]^45 // CoefficientList[#, q]& (* Jean-François Alcover, Aug 26 2019 *)

Prog

(PARI) seq(n)=Vec((sum(k=0, sqrtint(n), x^(k^2)) + O(x*x^n))^6) \\ Andrew Howroyd, Aug 08 2018

Crossrefs

Sequence in context: A280719 A282173 A328226 * A335268 A294651 A368309

Adjacent sequences: A045845 A045846 A045847 * A045849 A045850 A045851

Keyword

nonn

Author

N. J. A. Sloane

Status

approved