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A341404
Number of nonnegative solutions to (x_1)^2 + (x_2)^2 + ... + (x_9)^2 <= n.
3
1, 10, 46, 130, 265, 463, 799, 1339, 2014, 2780, 3860, 5444, 7301, 9263, 11783, 15263, 19250, 23237, 27893, 34193, 41519, 48701, 56765, 67421, 79484, 91067, 103739, 119855, 138035, 155819, 174923, 198863, 225890, 251444, 277976, 311492, 349122, 384420, 421284
OFFSET
0,2
COMMENTS
Partial sums of A045851.
FORMULA
G.f.: (1 + theta_3(x))^9 / (512 * (1 - x)).
a(n^2) = A055408(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, 9)+`if`(n>0, a(n-1), 0) end:
seq(a(n), n=0..38); # Alois P. Heinz, Feb 10 2021
MATHEMATICA
nmax = 38; CoefficientList[Series[(1 + EllipticTheta[3, 0, x])^9/(512 (1 - x)), {x, 0, nmax}], x]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 10 2021
STATUS
approved