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 A153361 #22 Apr 05 2024 09:58:26
%S A153361 12,22,42,80,154,296,572,1104,2138,4136,8020,15536,30148,58450,113472,
%T A153361 220110,427410,829352,1610628,3125954,6071028,11784514,22887536,
%U A153361 44431506,86293452,167532792,325373382,631721620,1226878704,2382108386
%N A153361 Number of zig-zag paths from top to bottom of a rectangle of width 12 with n rows.
%C A153361 Number of words of length n using a 12-symbol alphabet where neighboring letters are neighbors in the alphabet. - _Andrew Howroyd_, Apr 17 2017
%H A153361 Joseph Myers, <a href="http://www.polyomino.org.uk/publications/2008/bmo1-2009-q1.pdf">BMO 2008--2009 Round 1 Problem 1---Generalisation</a>
%H A153361 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,5,-4,-6,3,1).
%F A153361 G.f.: -2*x*(3*x^5 + 12*x^4 - 12*x^3 - 20*x^2 + 5*x + 6)/(x^6 + 3*x^5 - 6*x^4 - 4*x^3 + 5*x^2 + x - 1). - _Colin Barker_, Sep 02 2012
%t A153361 b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i == 0, Sum[b[n - 1, j, k], {j, 1, k}], If[i > 1, b[n - 1, i - 1, k], 0] + If[i < k, b[n - 1, i + 1, k], 0]]]; a[n_] := b[n, 0, 12]; Array[a, 30] (* _Jean-François Alcover_, Oct 10 2017, after _Alois P. Heinz_ *)
%Y A153361 Column 12 of A220062.
%Y A153361 Twice A129638.
%K A153361 easy,nonn
%O A153361 1,1
%A A153361 _Joseph Myers_, Dec 24 2008