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 A014110 #23 Aug 15 2025 10:30:37
%S A014110 1,4,6,4,5,12,12,4,6,16,18,12,8,16,24,12,5,24,30,16,18,28,24,12,12,28,
%T A014110 42,28,12,36,48,16,6,36,42,36,29,28,48,28,18,48,60,28,24,60,48,24,8,
%U A014110 44,72,48,30,48,84,36,24,52,54,48,36,52,72,52,5,72,96,40,42,72
%N A014110 Number of ordered ways of writing n as a sum of 4 squares of nonnegative integers.
%C A014110 This counts ordered sums of squares of nonnegative integers, whereas A000118 counts ordered sums of squares of integers of any sign. - _R. J. Mathar_, May 16 2023
%H A014110 T. D. Noe, <a href="/A014110/b014110.txt">Table of n, a(n) for n = 0..10000</a>
%H A014110 <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%F A014110 Coefficient of q^n in (1/16)*(1 + theta_3(0, q))^4; or coeff. of q^n in (Sum q^(i^2), i=0..inf)^4.
%e A014110 From _R. J. Mathar_, May 16 2023: (Start)
%e A014110 a(1)=4 counts 0^2+0^2+0^2+1^2 = 0^2+0^2+1^2+0^2 = 0^2+1^2+0^2+0^2 = 1^2+0^2+0^2+0^2.
%e A014110 a(2)=6 counts 0^2+0^2+1^2+1^2 = 0^2+1^2+0^2+1^2 = 0^2+1^2+1^2+0^2 = 1^2+0^2+0^2+1^2 = 1^2+0^2+1^2+0^2 = 1^2+1^2+0^2+0^2. (End)
%t A014110 a = Compile[{{n, _Integer}}, Block[{c = 0, k, j, i = Floor[Sqrt[n]]}, While[i > -1, j = Floor[Sqrt[n - i^2]]; While[j > -1, k = Floor[Sqrt[n - i^2 - j^2]]; While[k > -1, c += Boole[ Mod[ Sqrt[ n - i^2 - j^2 - k^2], 1] == 0]; k--]; j--]; i--]; c]]; Array[a, 70, 0] - (* _Robert G. Wilson v_, Aug 13 2025 *)
%Y A014110 Convolution square of A000925.
%K A014110 easy,nonn
%O A014110 0,2
%A A014110 Joe Keane (jgk(AT)jgk.org)