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%I #9 Oct 28 2015 11:42:53
%S 0,4,12,84,548,4172,33984,315800,3213032
%N Number of permutations of [n] with no carrier element, that is, having their exterior (longest pattern that is both a proper prefix and a proper suffix) contained in their interior (permutation obtained by deleting the first and the last entry) as a consecutive pattern.
%H Antonio Bernini, Luca Ferrari, and Einar Steingrímsson, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v18i1p146/0">The Möbius function of the consecutive pattern poset</a>, Electron. J. Combin., 18(1):Paper 146, 12 pp., 2011.
%H Sergi Elizalde, Peter R. W. McNamara, <a href="http://arxiv.org/abs/1508.05963">The structure of the consecutive pattern poset</a>, arXiv:1508.05963 [math.CO], 2015.
%H Bruce E. Sagan and Robert Willenbring, <a href="http://dx.doi.org/10.1007/s10801-012-0347-3">Discrete Morse theory and the consecutive pattern poset</a>, J. Algebraic Combin., 36(4):501-514, 2012.
%e For n=3, we have a(3)=4 because the permutations 132, 213, 231, 312 have exterior equal to 1, and thus contained in their interior. On the other hand, 123 has exterior 12, and 321 has exterior 21.
%K nonn,more
%O 2,2
%A _Sergi Elizalde_, Oct 28 2015