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A340947 Number of ways to write n as an ordered sum of 10 squares of positive integers.

%I A340947 #12 Feb 04 2021 15:27:20
%S A340947 1,0,0,10,0,0,45,0,10,120,0,90,210,0,360,262,45,840,300,360,1260,480,
%T A340947 1260,1350,1015,2520,1560,2200,3150,2880,4186,2880,5430,6240,3780,
%U A340947 8300,7080,7920,11160,7320,13257,14640,10600,16470,18570,18240,19620,22230,25135,27720,28020,28480,38160
%N A340947 Number of ways to write n as an ordered sum of 10 squares of positive integers.
%H A340947 David A. Corneth, <a href="/A340947/b340947.txt">Table of n, a(n) for n = 10..10009</a>
%H A340947 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A340947 G.f.: (theta_3(x) - 1)^10 / 1024, where theta_3() is the Jacobi theta function.
%p A340947 b:= proc(n, t) option remember;
%p A340947       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->
%p A340947       `if`(s>n, 0, b(n-s, t-1)))(j^2), j=1..isqrt(n))))
%p A340947     end:
%p A340947 a:= n-> b(n, 10):
%p A340947 seq(a(n), n=10..62);  # _Alois P. Heinz_, Jan 31 2021
%t A340947 nmax = 62; CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^10/1024, {x, 0, nmax}], x] // Drop[#, 10] &
%Y A340947 Cf. A000144, A000290, A010052, A025434, A045852, A063691, A063725, A063730, A340481, A340905, A340906, A340915, A340946.
%Y A340947 Column k=10 of A337165.
%K A340947 nonn
%O A340947 10,4
%A A340947 _Ilya Gutkovskiy_, Jan 31 2021