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 A356251 #34 Jun 20 2025 08:21:46
%S A356251 0,6,50,210,630,1540,3276,6300,11220,18810,30030,46046,68250,98280,
%T A356251 138040,189720,255816,339150,442890,570570,726110,913836,1138500,
%U A356251 1405300,1719900,2088450,2517606,3014550,3587010,4243280,4992240,5843376,6806800,7893270,9114210
%N A356251 a(n) = n*(n+1)*(n+2)*(n+3)*(2*n+1)/12.
%C A356251 Sum of all numbers squared in ordered triples (x,y,z) where 0 <= x <= y <= z <= n.
%H A356251 Edward Krogius, <a href="/A356251/b356251.txt">Table of n, a(n) for n = 0..999</a>
%H A356251 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A356251 G.f.: 2*x*(7*x+3)/(x-1)^6.
%F A356251 From _Amiram Eldar_, Sep 11 2022: (Start)
%F A356251 Sum_{n>=1} 1/a(n) = 136/15 - 64*log(2)/5.
%F A356251 Sum_{n>=1} (-1)^(n+1)/a(n) = 16*Pi/5 - 32*log(2)/5 - 82/15. (End)
%e A356251 a(1) = 6 because we have the triples (0,0,0), (0,0,1), (0,1,1), (1,1,1).
%t A356251 Table[n*(n + 1)*(n + 2)*(n + 3)*(2*n + 1)/12, {n, 0, 35}] (* _Amiram Eldar_, Sep 11 2022 *)
%t A356251 Table[Sum[x^2 + y^2 + z^2, {x, 0, g}, {y, x, g}, {z, y, g}], {g, 0, 30}] (* _Horst H. Manninger_, Jun 19 2025 *)
%Y A356251 Cf. A033487.
%K A356251 nonn,easy
%O A356251 0,2
%A A356251 _Edward Krogius_, Jul 31 2022