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A340905
Number of ways to write n as an ordered sum of 6 squares of positive integers.
11
1, 0, 0, 6, 0, 0, 15, 0, 6, 20, 0, 30, 15, 0, 60, 12, 15, 60, 31, 60, 30, 60, 90, 36, 86, 60, 120, 120, 15, 180, 141, 60, 165, 140, 180, 186, 120, 180, 285, 156, 126, 360, 255, 216, 270, 260, 390, 240, 262, 420, 426, 360, 210, 540, 530, 216, 540, 540, 480, 600, 300, 600, 825, 312, 576, 840
OFFSET
6,4
FORMULA
G.f.: (theta_3(x) - 1)^6 / 64, where theta_3() is the Jacobi theta function.
MAPLE
b:= proc(n, t) option remember;
`if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->
`if`(s>n, 0, b(n-s, t-1)))(j^2), j=1..isqrt(n))))
end:
a:= n-> b(n, 6):
seq(a(n), n=6..71); # Alois P. Heinz, Jan 31 2021
MATHEMATICA
nmax = 71; CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^6/64, {x, 0, nmax}], x] // Drop[#, 6] &
KEYWORD
nonn,look
AUTHOR
Ilya Gutkovskiy, Jan 31 2021
STATUS
approved