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%I #9 Sep 14 2021 20:49:45
%S 1,1,1,7,8,9,25,32,46,76,102,165,233,317,488,690,971,1395,1991,2850,
%T 4024,5721,8144,11550,16396,23225,32987,46814,66315,94069,133415,
%U 189148,268181,380227,539114,764387,1083692,1536369,2178299,3088302,4378362,6207477
%N Expansion of (theta_3(x) - 1)^6 / (32 * (3 - theta_3(x))).
%C Number of compositions (ordered partitions) of n into 6 or more squares.
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F a(n) = Sum_{k=6..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, 6):
%p seq(a(n), n=6..47); # _Alois P. Heinz_, Sep 14 2021
%t nmax = 47; CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^6/(32 (3 - EllipticTheta[3, 0, x])), {x, 0, nmax}], x] // Drop[#, 6] &
%Y Cf. A000290, A006456, A337165, A347805, A347806, A347807, A347808.
%K nonn
%O 6,4
%A _Ilya Gutkovskiy_, Sep 14 2021