%I #27 Aug 24 2020 09:41:48

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

%N The number of permutations avoiding the "boxed" pattern 123.

%C 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

%H Sergey Avgustinovich, Sergey Kitaev and Alexander Valyuzhenich, <a href="http://personal.strath.ac.uk/sergey.kitaev/Papers/mesh.pdf">Avoidance of boxed mesh patterns on permutations</a>.

%t 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]

%K nonn,more

%O 0,3

%A _N. J. A. Sloane_, May 06 2012

%E More terms and Mathematica program from _Peter J. Taylor_, Apr 27 2015