This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A341401 #7 Feb 10 2021 20:40:00
%S A341401 1,7,22,42,63,99,160,220,265,337,457,577,672,792,978,1178,1319,1469,
%T A341401 1739,2039,2255,2507,2882,3242,3513,3819,4269,4769,5159,5555,6181,
%U A341401 6841,7246,7666,8401,9181,9763,10363,11188,12108,12828,13434,14394,15534,16359,17211,18477,19677
%N A341401 Number of nonnegative solutions to (x_1)^2 + (x_2)^2 + ... + (x_6)^2 <= n.
%C A341401 Partial sums of A045848.
%H A341401 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A341401 G.f.: (1 + theta_3(x))^6 / (64 * (1 - x)).
%F A341401 a(n^2) = A055405(n).
%p A341401 b:= proc(n, k) option remember; `if`(n=0, 1, `if`(n<0 or k<1, 0,
%p A341401 b(n, k-1)+add(b(n-j^2, k-1), j=1..isqrt(n))))
%p A341401 end:
%p A341401 a:= proc(n) option remember; b(n, 6)+`if`(n>0, a(n-1), 0) end:
%p A341401 seq(a(n), n=0..47); # _Alois P. Heinz_, Feb 10 2021
%t A341401 nmax = 47; CoefficientList[Series[(1 + EllipticTheta[3, 0, x])^6/(64 (1 - x)), {x, 0, nmax}], x]
%Y A341401 Cf. A000122, A000606, A003059, A045848, A055405, A055412, A175361, A224212, A224213, A302862, A341400, A341402.
%K A341401 nonn
%O A341401 0,2
%A A341401 _Ilya Gutkovskiy_, Feb 10 2021