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 A374397 #20 Sep 23 2024 07:57:50
%S A374397 2,100,726,2696,7210,15852,30590,53776,88146,136820,203302,291480,
%T A374397 405626,550396,730830,952352,1220770,1542276,1923446,2371240,2893002,
%U A374397 3496460,4189726,4981296,5880050,6895252,8036550,9313976,10737946,12319260,14069102,15999040,18121026
%N A374397 a(n) is the number of 4-step self avoiding walks in the n-dimensional hypercubic lattice that start at the origin.
%C A374397 We have the formula below because we have 2*n choices for the first step, and (2*n-1)^3 choices for the next three, but have counted exactly 2*n*(2*n-1)*(2*n-2) self-intersecting walks.
%D A374397 N. Madras and G. Slade, "The Self Avoiding Walk", Birkhäuser, 2013.
%H A374397 Paolo Xausa, <a href="/A374397/b374397.txt">Table of n, a(n) for n = 1..10000</a>
%H A374397 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A374397 a(n) = 16*n^4 - 24*n^3 + 8*n^2 + 2*n.
%F A374397 G.f.: 2*x*(1 + 45*x + 123*x^2 + 23*x^3)/(1 - x)^5. - _Stefano Spezia_, Jul 07 2024
%t A374397 A374397[n_] := 2*n*(4*n*(n - 1)*(2*n - 1) + 1);
%t A374397 Array[A374397, 50] (* or *)
%t A374397 LinearRecurrence[{5, -10, 10, -5, 1}, {2, 100, 726, 2696, 7210}, 50] (* _Paolo Xausa_, Sep 23 2024 *)
%Y A374397 Cf. A010575.
%K A374397 nonn,walk,easy
%O A374397 1,1
%A A374397 _Johann Peters_, Jul 07 2024