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A340915 Number of ways to write n as an ordered sum of 8 squares of positive integers.

%I A340915 #12 Feb 04 2021 15:26:34
%S A340915 1,0,0,8,0,0,28,0,8,56,0,56,70,0,168,64,28,280,84,168,280,176,420,224,
%T A340915 345,560,392,616,420,848,924,336,1246,1064,868,1464,988,1680,1820,
%U A340915 1120,1904,2464,1932,1904,2870,2752,2772,2912,2892,4256,3640,3248,4480,5040,4760,3696,6120
%N A340915 Number of ways to write n as an ordered sum of 8 squares of positive integers.
%H A340915 Alois P. Heinz, <a href="/A340915/b340915.txt">Table of n, a(n) for n = 8..20000</a>
%H A340915 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A340915 G.f.: (theta_3(x) - 1)^8 / 256, where theta_3() is the Jacobi theta function.
%p A340915 b:= proc(n, t) option remember;
%p A340915       `if`(n=0, `if`(t=0, 1, 0), `if`(t<1, 0, add((s->
%p A340915       `if`(s>n, 0, b(n-s, t-1)))(j^2), j=1..isqrt(n))))
%p A340915     end:
%p A340915 a:= n-> b(n, 8):
%p A340915 seq(a(n), n=8..64);  # _Alois P. Heinz_, Jan 31 2021
%t A340915 nmax = 64; CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^8/256, {x, 0, nmax}], x] // Drop[#, 8] &
%Y A340915 Cf. A000143, A000290, A010052, A025432, A045850, A063691, A063725, A063730, A340481, A340905, A340906, A340946, A340947.
%Y A340915 Column k=8 of A337165.
%K A340915 nonn
%O A340915 8,4
%A A340915 _Ilya Gutkovskiy_, Jan 31 2021