

A111281


Number of permutations avoiding the patterns {2413,2431,4213,3412,3421,4231,4321,4312}; number of strong sorting class based on 2413.


1



1, 1, 2, 6, 16, 40, 100, 252, 636, 1604, 4044, 10196, 25708, 64820, 163436, 412084, 1039020, 2619764, 6605420, 16654772, 41993004, 105880308, 266964460, 673118772, 1697188012, 4279255412, 10789627756, 27204748468, 68593500716, 172950260724, 436073277676
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OFFSET

0,3


COMMENTS

a(n) = term (1,1) in M^n, M = the 4x4 matrix [1,1,1,1; 0,1,0,1; 0,0,1,1; 1,0,0,1].  Gary W. Adamson, Apr 29 2009
Number of permutations of length n>0 avoiding the partially ordered pattern (POP) {1>2, 1>4} of length 4. That is, number of length n permutations having no subsequences of length 4 in which the first element is larger than the second and fourth elements.  Sergey Kitaev, Dec 09 2020


LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..2490
M. Albert, R. Aldred, M. Atkinson, C Handley, D. Holton, D. McCaughan and H. van Ditmarsch, Sorting Classes, Elec. J. of Comb. 12 (2005) R31.
Alice L. L. Gao, Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, arXiv:1903.08946 [math.CO], 2019.
Alice L. L. Gao, Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, The Electronic Journal of Combinatorics 26(3) (2019), P3.26.
Kai Ting Keshia Yap, David Wehlau, and Imed Zaguia, Permutations Avoiding Certain Partiallyordered Patterns, arXiv:2101.12061 [math.CO], 2021.
Index entries for linear recurrences with constant coefficients, signature (3,2,2).


FORMULA

a(n) = 3*a(n1)2*a(n2)+2*a(n3).
G.f.: 1+x*(1x+2*x^2)/(13*x+2*x^22*x^3).  Colin Barker, Jan 16 2012


MATHEMATICA

a[1] = 1; a[2] = 2; a[3] = 6; a[n_] := a[n] = 3a[n  1]  2a[n  2] + 2a[n  3]; Table[a[n], {n, 28}] (* Robert G. Wilson v *)


CROSSREFS

Sequence in context: A264551 A293004 A265278 * A018021 A215340 A074405
Adjacent sequences: A111278 A111279 A111280 * A111282 A111283 A111284


KEYWORD

nonn,easy


AUTHOR

Len Smiley, Nov 01 2005


EXTENSIONS

More terms from Robert G. Wilson v, Nov 04 2005
a(0)=1 prepended by Alois P. Heinz, May 07 2021


STATUS

approved



