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A341405 Number of nonnegative solutions to (x_1)^2 + (x_2)^2 + ... + (x_10)^2 <= n.

%I A341405 #5 Feb 10 2021 20:45:38
%S A341405 1,11,56,176,396,738,1308,2268,3618,5258,7449,10689,14889,19609,25369,
%T A341405 33289,43154,53774,65739,81339,100671,121221,143421,171501,205701,
%U A341405 241283,278678,324398,378998,435968,495428,566468,650798,737888,826083,930123,1053323
%N A341405 Number of nonnegative solutions to (x_1)^2 + (x_2)^2 + ... + (x_10)^2 <= n.
%C A341405 Partial sums of A045852.
%H A341405 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A341405 G.f.: (1 + theta_3(x))^10 / (1024 * (1 - x)).
%F A341405 a(n^2) = A055409(n).
%p A341405 b:= proc(n, k) option remember; `if`(n=0, 1, `if`(n<0 or k<1, 0,
%p A341405       b(n, k-1)+add(b(n-j^2, k-1), j=1..isqrt(n))))
%p A341405     end:
%p A341405 a:= proc(n) option remember; b(n, 10)+`if`(n>0, a(n-1), 0) end:
%p A341405 seq(a(n), n=0..36);  # _Alois P. Heinz_, Feb 10 2021
%t A341405 nmax = 36; CoefficientList[Series[(1 + EllipticTheta[3, 0, x])^10/(1024 (1 - x)), {x, 0, nmax}], x]
%Y A341405 Cf. A000122, A000606, A003059, A045852, A055409, A055416, A224212, A224213, A302862, A341400, A341401, A341402, A341403, A341404.
%K A341405 nonn
%O A341405 0,2
%A A341405 _Ilya Gutkovskiy_, Feb 10 2021