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A340947
Number of ways to write n as an ordered sum of 10 squares of positive integers.
10
1, 0, 0, 10, 0, 0, 45, 0, 10, 120, 0, 90, 210, 0, 360, 262, 45, 840, 300, 360, 1260, 480, 1260, 1350, 1015, 2520, 1560, 2200, 3150, 2880, 4186, 2880, 5430, 6240, 3780, 8300, 7080, 7920, 11160, 7320, 13257, 14640, 10600, 16470, 18570, 18240, 19620, 22230, 25135, 27720, 28020, 28480, 38160
OFFSET
10,4
FORMULA
G.f.: (theta_3(x) - 1)^10 / 1024, 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, 10):
seq(a(n), n=10..62); # Alois P. Heinz, Jan 31 2021
MATHEMATICA
nmax = 62; CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^10/1024, {x, 0, nmax}], x] // Drop[#, 10] &
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 31 2021
STATUS
approved