OFFSET
0,5
COMMENTS
The number of integer solutions is given by A033716.
Records 1, 2, 3, 5, 6, 9, 12, 14, 18, ... occur at 0, 4, 28, 196, 364, 2548, 6916, 33124, 48412, ... - Antti Karttunen, Nov 20 2017
LINKS
Antti Karttunen, Table of n, a(n) for n = 0..65537
N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)
FORMULA
For n > 0, a(n) = (A033716(n) + 2)/4 if n is a square or a triple of a square; otherwise a(n) = A033716(n)/4. Alternatively, a(n) = ceiling(A033716(n)/4).
G.f.: (1 + theta_3(q))*(1 + theta_3(q^3))/4, where theta_3() is the Jacobi theta function. - Ilya Gutkovskiy, Aug 01 2018
MATHEMATICA
QP = QPochhammer;
s = (QP[q^2]*QP[q^6])^5/(QP[q]*QP[q^3]*QP[q^4]*QP[q^12])^2 + O[q]^105;
A033716 = CoefficientList[s, q];
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Max Alekseyev, May 16 2006
STATUS
approved