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.

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

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 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.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..50

Crossrefs

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

Sequence in context: A370089 A193253 A272126 * A347504 A061657 A217301

Adjacent sequences: A171560 A171561 A171562 * A171564 A171565 A171566

Keyword

nonn,walk

Author

Lee A. Newberg, Dec 11 2009

Extensions

Extended beyond a(9) by Alois P. Heinz, Jan 22 2013

Status

approved