

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.


3



1, 1, 183, 12645, 985035, 81827267, 7118644591, 640769321689, 59196873690319, 5581678517756599, 535018115452292125, 51979823843828063203, 5107397983259866484167, 506660924932346216388835, 50675683529411401757497171, 5104747391125384906330663869
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OFFSET

0,3


COMMENTS

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 nongap 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 ith position of some string x is in the same column as some jth position of some string y.


LINKS



CROSSREFS

See A171155 and A171158 for the number of such walks in two dimensions and in three dimensions.


KEYWORD

nonn,walk


AUTHOR



EXTENSIONS



STATUS

approved



