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A340946 Number of ways to write n as an ordered sum of 9 squares of positive integers.

%I A340946 #10 Feb 04 2021 15:26:57
%S A340946 1,0,0,9,0,0,36,0,9,84,0,72,126,0,252,135,36,504,156,252,630,288,756,
%T A340946 576,606,1260,756,1207,1260,1584,2052,1008,2727,2688,1764,3663,2718,
%U A340946 3816,4608,2853,5418,6048,4620,5868,7506,7464,7308,8442,8958,11088,10404,9684,13986,14184,13020
%N A340946 Number of ways to write n as an ordered sum of 9 squares of positive integers.
%H A340946 Alois P. Heinz, <a href="/A340946/b340946.txt">Table of n, a(n) for n = 9..20000</a>
%H A340946 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A340946 G.f.: (theta_3(x) - 1)^9 / 512, where theta_3() is the Jacobi theta function.
%p A340946 b:= proc(n, t) option remember;
%p A340946       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->
%p A340946       `if`(s>n, 0, b(n-s, t-1)))(j^2), j=1..isqrt(n))))
%p A340946     end:
%p A340946 a:= n-> b(n, 9):
%p A340946 seq(a(n), n=9..63);  # _Alois P. Heinz_, Jan 31 2021
%t A340946 nmax = 63; CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^9/512, {x, 0, nmax}], x] // Drop[#, 9] &
%Y A340946 Cf. A000290, A008452, A010052, A025433, A045851, A063691, A063725, A063730, A340481, A340905, A340906, A340915, A340947.
%Y A340946 Column k=9 of A337165.
%K A340946 nonn
%O A340946 9,4
%A A340946 _Ilya Gutkovskiy_, Jan 31 2021