OFFSET
0,2
LINKS
Nian Hong Zhou, Yalin Sun, Counting the number of solutions to certain infinite Diophantine equations, arXiv:1910.07884 [math.NT], 2019.
FORMULA
a(n) = [q^n] Product_{j>0} Product_{n>0} (1 - (-1)^n*q^(n*j^r)) / (1 + (-1)^n*q^(n*j^r)) with r = 2 (see Proposition 1.1 in Zhou and Sun).
EXAMPLE
a(16) = 6 since there are 6 integer solutions to 1^2*k1^2 + 2^2*k2^2 + 3^2*k3^2 + 4^2*k4^2 + ... = 16:
k1 = +-4 and k_j = 0 for j > 1;
k1 = 0, k2 = +-2 and k_j = 0 for j > 2;
k1 = k2 = k3 = 0, k4 = +-1 and k_j = 0 for j > 4.
MATHEMATICA
nmax=70; r=2; CoefficientList[Series[Product[Product[(1-(-1)^n*q^(n*j^r))/(1+(-1)^n*q^(n*j^r)), {n, 1, nmax}], {j, 1, nmax}], {q, 0, nmax}], q]
CROSSREFS
KEYWORD
nonn
AUTHOR
Stefano Spezia, Nov 09 2019
STATUS
approved