A201168 The number of permutations avoiding the "boxed" pattern 123.

1, 1, 2, 5, 15, 51, 194, 810, 3675, 17935, 93481, 517129, 3021133

Offset

0,3

Comments

The statement in the Avgustinovich, Kitaev and Valyuzhenich paper that a(6) is greater than 303 is easily seen to be wrong, since that would require (among other constraints) that no more than 2 boxed-123-avoiding permutations of length 5 end in an ascent. - Peter J. Taylor, Apr 27 2015

Links

Table of n, a(n) for n=0..12.

Sergey Avgustinovich, Sergey Kitaev and Alexander Valyuzhenich, Avoidance of boxed mesh patterns on permutations.

Mathematica

valid[l_] := valid[l] = Which[Length@l<3, True, Length@l==3, !Less@@l, True, valid[Most@l]&&valid[Rest@l]&&valid[DeleteCases[l, Min@l]]&&valid[DeleteCases[l, Max@l]]]; Length@Select[Permutations@Range@#, valid] & /@ Range[0, 9]

Crossrefs

Sequence in context: A304454 A287253 A117426 * A001681 A343665 A192553

Adjacent sequences: A201165 A201166 A201167 * A201169 A201170 A201171

Keyword

nonn,more

Author

N. J. A. Sloane, May 06 2012

Extensions

More terms and Mathematica program from Peter J. Taylor, Apr 27 2015

Status

approved