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A341424
Number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_5)^2 <= n^2.
7
6, 51, 177, 547, 1348, 2958, 5574, 10084, 16974, 27450, 41970, 62671, 90216, 128082, 175867, 238018, 316373, 414998, 534094, 682144, 859705, 1075165, 1326551, 1627896, 1976582, 2390057, 2862607, 3411273, 4039483, 4760419, 5571729, 6500650, 7541560, 8722096
OFFSET
3,1
FORMULA
a(n) is the coefficient of x^(n^2) in expansion of (theta_3(x) - 1)^5 / (32 * (1 - x)).
MAPLE
b:= proc(n, k) option remember; `if`(k=0, 1, `if`(n=0, 0,
add((s->`if`(s>n, 0, b(n-s, k-1)))(j^2), j=1..isqrt(n))))
end:
a:= n-> b(n^2, 5):
seq(a(n), n=3..36); # Alois P. Heinz, Feb 11 2021
MATHEMATICA
Table[SeriesCoefficient[(EllipticTheta[3, 0, x] - 1)^5/(32 (1 - x)), {x, 0, n^2}], {n, 3, 36}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 11 2021
STATUS
approved