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A340947
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Number of ways to write n as an ordered sum of 10 squares of positive integers.
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10
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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
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OFFSET
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10,4
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LINKS
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David A. Corneth, Table of n, a(n) for n = 10..10009
Index entries for sequences related to sums of squares
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FORMULA
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G.f.: (theta_3(x) - 1)^10 / 1024, where theta_3() is the Jacobi theta function.
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MAPLE
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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
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MATHEMATICA
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nmax = 62; CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^10/1024, {x, 0, nmax}], x] // Drop[#, 10] &
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CROSSREFS
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Cf. A000144, A000290, A010052, A025434, A045852, A063691, A063725, A063730, A340481, A340905, A340906, A340915, A340946.
Column k=10 of A337165.
Sequence in context: A287734 A064511 A341809 * A306934 A003785 A287711
Adjacent sequences: A340944 A340945 A340946 * A340948 A340949 A340950
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KEYWORD
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nonn
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AUTHOR
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Ilya Gutkovskiy, Jan 31 2021
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STATUS
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approved
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