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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 (list; graph; refs; listen; history; text; internal format)
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 Partially-ordered Patterns, arXiv:2101.12061 [math.CO], 2021.

Index entries for linear recurrences with constant coefficients, signature (3,-2,2).

FORMULA

a(n) = 3*a(n-1)-2*a(n-2)+2*a(n-3).

G.f.: 1+x*(1-x+2*x^2)/(1-3*x+2*x^2-2*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

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Last modified October 20 18:43 EDT 2021. Contains 348118 sequences. (Running on oeis4.)