OFFSET
0,2
COMMENTS
Partial sums of A008451.
FORMULA
G.f.: theta_3(x)^7 / (1 - x).
a(n^2) = A055413(n).
MAPLE
b:= proc(n, k) option remember; `if`(n=0, 1, `if`(n<0 or k<1, 0,
b(n, k-1)+2*add(b(n-j^2, k-1), j=1..isqrt(n))))
end:
a:= proc(n) option remember; b(n, 7)+`if`(n>0, a(n-1), 0) end:
seq(a(n), n=0..35); # Alois P. Heinz, Feb 10 2021
MATHEMATICA
nmax = 35; CoefficientList[Series[EllipticTheta[3, 0, x]^7/(1 - x), {x, 0, nmax}], x]
Table[SquaresR[7, n], {n, 0, 35}] // Accumulate
PROG
(PARI) my(q='q+O('q^(55))); Vec((eta(q^2)^5/(eta(q)^2*eta(q^4)^2))^7/(1-q)) \\ Joerg Arndt, Jun 21 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 10 2021
STATUS
approved