login
A341403
Number of nonnegative solutions to (x_1)^2 + (x_2)^2 + ... + (x_8)^2 <= n.
3
1, 9, 37, 93, 171, 283, 479, 767, 1076, 1420, 1952, 2688, 3444, 4228, 5320, 6776, 8262, 9662, 11454, 13918, 16480, 18832, 21772, 25644, 29508, 33044, 37300, 42732, 48340, 53556, 59632, 67472, 75405, 82237, 90189, 100661, 111155, 120403, 131099, 144651, 158469, 170621
OFFSET
0,2
COMMENTS
Partial sums of A045850.
FORMULA
G.f.: (1 + theta_3(x))^8 / (256 * (1 - x)).
a(n^2) = A055407(n).
MAPLE
b:= proc(n, k) option remember; `if`(n=0, 1, `if`(n<0 or k<1, 0,
b(n, k-1)+add(b(n-j^2, k-1), j=1..isqrt(n))))
end:
a:= proc(n) option remember; b(n, 8)+`if`(n>0, a(n-1), 0) end:
seq(a(n), n=0..41); # Alois P. Heinz, Feb 10 2021
MATHEMATICA
nmax = 41; CoefficientList[Series[(1 + EllipticTheta[3, 0, x])^8/(256 (1 - x)), {x, 0, nmax}], x]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 10 2021
STATUS
approved