login
A341425
Number of positive solutions to (x_1)^2 + (x_2)^2 + ... + (x_6)^2 <= n^2.
7
7, 48, 331, 1269, 3698, 9382, 20927, 42683, 79844, 142173, 238810, 387615, 603589, 915324, 1345294, 1939221, 2729723, 3783313, 5138567, 6895632, 9108626, 11909496, 15362753, 19642539, 24832744, 31179476, 38757032, 47877886, 58647957, 71447776, 86391220
OFFSET
3,1
FORMULA
a(n) is the coefficient of x^(n^2) in expansion of (theta_3(x) - 1)^6 / (64 * (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, 6):
seq(a(n), n=3..33); # Alois P. Heinz, Feb 11 2021
MATHEMATICA
Table[SeriesCoefficient[(EllipticTheta[3, 0, x] - 1)^6/(64 (1 - x)), {x, 0, n^2}], {n, 3, 33}]
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 11 2021
STATUS
approved