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%I #10 Sep 14 2021 20:48:34
%S 1,1,1,4,5,6,10,14,22,30,41,62,88,123,173,248,354,500,710,1006,1427,
%T 2024,2867,4066,5767,8176,11591,16436,23301,33032,46832,66396,94137,
%U 133461,189209,268252,380315,539190,764431,1083764,1536498,2178364,3088363,4378502,6207581
%N Expansion of (theta_3(x) - 1)^3 / (4 * (3 - theta_3(x))).
%C Number of compositions (ordered partitions) of n into 3 or more squares.
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F a(n) = Sum_{k=3..n} A337165(n,k). - _Alois P. Heinz_, Sep 14 2021
%p b:= proc(n, t) option remember; `if`(n=0, `if`(t=0, 1, 0), add((
%p s->`if`(s>n, 0, b(n-s, max(0, t-1))))(j^2), j=1..isqrt(n)))
%p end:
%p a:= n-> b(n, 3):
%p seq(a(n), n=3..47); # _Alois P. Heinz_, Sep 14 2021
%t nmax = 47; CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^3/(4 (3 - EllipticTheta[3, 0, x])), {x, 0, nmax}], x] // Drop[#, 3] &
%Y Cf. A000290, A006456, A337165, A347805, A347807, A347808, A347809.
%K nonn
%O 3,4
%A _Ilya Gutkovskiy_, Sep 14 2021
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