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A341428 Number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_9)^2 <= n^2. 7
1, 46, 760, 7751, 43910, 186098, 652710, 1943742, 5178030, 12411211, 27773308, 57798904, 114152429, 214399664, 387571706, 673189698, 1135916808, 1857320784, 2966816950, 4623984661, 7066527283, 10577150039, 15589368584, 22580091614, 32256768126 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,2
LINKS
FORMULA
a(n) is the coefficient of x^(n^2) in expansion of (theta_3(x) - 1)^9 / (512 * (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, 9):
seq(a(n), n=3..27); # Alois P. Heinz, Feb 11 2021
MATHEMATICA
Table[SeriesCoefficient[(EllipticTheta[3, 0, x] - 1)^9/(512 (1 - x)), {x, 0, n^2}], {n, 3, 27}]
CROSSREFS
Sequence in context: A224306 A224370 A078156 * A066405 A113922 A160067
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 11 2021
STATUS
approved

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Last modified July 13 17:35 EDT 2024. Contains 374284 sequences. (Running on oeis4.)