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 A171563 #9 Nov 14 2014 21:28:29 %S A171563 1,1,183,12645,985035,81827267,7118644591,640769321689,59196873690319, %T A171563 5581678517756599,535018115452292125,51979823843828063203, %U A171563 5107397983259866484167,506660924932346216388835,50675683529411401757497171,5104747391125384906330663869 %N A171563 The number of walks from (0,0,0,0) to (n,n,n,n) with steps that increment one to four coordinates and having the property that no two consecutive steps are orthogonal. %C A171563 a(n) is also the number of standard sequence alignments of four strings of length n, counting only those alignments with the property that, for every pair of consecutive alignment columns, there is at least one sequence that contributes a non-gap to both columns. That is, a(n) counts only those standard alignments with a column order that can be unambiguously reconstructed from the knowledge of all pairings, where a pairing is, e.g., that some i-th position of some string x is in the same column as some j-th position of some string y. %H A171563 Alois P. Heinz, <a href="/A171563/b171563.txt">Table of n, a(n) for n = 0..50</a> %Y A171563 See A171155 and A171158 for the number of such walks in two dimensions and in three dimensions. %K A171563 nonn,walk %O A171563 0,3 %A A171563 _Lee A. Newberg_, Dec 11 2009 %E A171563 Extended beyond a(9) by _Alois P. Heinz_, Jan 22 2013