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%I #10 Sep 14 2021 20:49:30
%S 1,1,1,6,7,8,19,25,37,56,76,122,170,233,347,494,700,991,1415,2021,
%T 2855,4054,5751,8164,11585,16406,23285,33032,46814,66375,94119,133445,
%U 189193,268231,380287,539184,764422,1083722,1536479,2178349,3088333,4378472,6207557
%N Expansion of (theta_3(x) - 1)^5 / (16 * (3 - theta_3(x))).
%C Number of compositions (ordered partitions) of n into 5 or more squares.
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F a(n) = Sum_{k=5..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, 5):
%p seq(a(n), n=5..47); # _Alois P. Heinz_, Sep 14 2021
%t nmax = 47; CoefficientList[Series[(EllipticTheta[3, 0, x] - 1)^5/(16 (3 - EllipticTheta[3, 0, x])), {x, 0, nmax}], x] // Drop[#, 5] &
%Y Cf. A000290, A006456, A337165, A347805, A347806, A347807, A347809.
%K nonn
%O 5,4
%A _Ilya Gutkovskiy_, Sep 14 2021
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