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A341399 Number of integer solutions to (x_1)^2 + (x_2)^2 + ... + (x_10)^2 <= n.

%I A341399 #8 Feb 10 2021 19:30:56
%S A341399 1,21,201,1161,4541,12965,29285,58085,110105,198765,327829,503509,
%T A341399 765589,1152509,1642109,2243069,3083569,4221529,5551949,7115789,
%U A341399 9166133,11777333,14763893,18121973,22316213,27634481,33512921,39812441,47674841,57294401,67510721,78592961
%N A341399 Number of integer solutions to (x_1)^2 + (x_2)^2 + ... + (x_10)^2 <= n.
%C A341399 Partial sums of A000144.
%H A341399 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A341399 G.f.: theta_3(x)^10 / (1 - x).
%F A341399 a(n^2) = A055416(n).
%p A341399 b:= proc(n, k) option remember; `if`(n=0, 1, `if`(n<0 or k<1, 0,
%p A341399       b(n, k-1)+2*add(b(n-j^2, k-1), j=1..isqrt(n))))
%p A341399     end:
%p A341399 a:= proc(n) option remember; b(n, 10)+`if`(n>0, a(n-1), 0) end:
%p A341399 seq(a(n), n=0..31);  # _Alois P. Heinz_, Feb 10 2021
%t A341399 nmax = 31; CoefficientList[Series[EllipticTheta[3, 0, x]^10/(1 - x), {x, 0, nmax}], x]
%t A341399 Table[SquaresR[10, n], {n, 0, 31}] // Accumulate
%Y A341399 Cf. A000122, A000144, A001650, A046895, A055409, A055416, A057655, A117609, A122510, A175360, A175361, A302860, A341396, A341397, A341398.
%K A341399 nonn
%O A341399 0,2
%A A341399 _Ilya Gutkovskiy_, Feb 10 2021