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A341398
Number of integer solutions to (x_1)^2 + (x_2)^2 + ... + (x_9)^2 <= n.
5
1, 19, 163, 835, 2869, 7189, 14581, 27253, 49861, 84663, 129303, 190071, 284055, 409335, 550455, 732855, 995241, 1312617, 1656153, 2077497, 2634777, 3300057, 4003641, 4804281, 5872665, 7129227, 8363307, 9784491, 11635755, 13670475, 15727755, 18066315, 20950491
OFFSET
0,2
COMMENTS
Partial sums of A008452.
FORMULA
G.f.: theta_3(x)^9 / (1 - x).
a(n^2) = A055415(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, 9)+`if`(n>0, a(n-1), 0) end:
seq(a(n), n=0..32); # Alois P. Heinz, Feb 10 2021
MATHEMATICA
nmax = 32; CoefficientList[Series[EllipticTheta[3, 0, x]^9/(1 - x), {x, 0, nmax}], x]
Table[SquaresR[9, n], {n, 0, 32}] // Accumulate
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 10 2021
STATUS
approved