OFFSET
0,2
COMMENTS
More generally, the ordinary generating function for the number of ways of writing n as a sum of k squares is theta_3(0, q)^k = 1 + 2*k*q + 2*(k - 1)*k*q^2 + (4/3)*(k - 2)*(k - 1)*k*q^3 + (2/3)*((k - 3)*(k - 2)*(k - 1) + 3)*k*q^4 + (4/15) *(k - 1)*k*(k^3 - 9*k^2 + 26*k - 9)*q^5 + ..., where theta is the Jacobi theta functions.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Sum of Squares Function
Eric Weisstein's World of Mathematics, Jacobi Theta Functions
FORMULA
G.f.: theta_3(0,q)^13, where theta_3(x,q) is the third Jacobi theta function.
a(n) = (26/n)*Sum_{k=1..n} A186690(k)*a(n-k), a(0) = 1. - Seiichi Manyama, May 27 2017
MATHEMATICA
Table[SquaresR[13, n], {n, 0, 26}]
CROSSREFS
13th column of A286815. - Seiichi Manyama, May 27 2017
Row d=13 of A122141.
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Aug 27 2016
STATUS
approved