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A179257 Number of permutations of length n which avoid the patterns 321 and 1324. 0
1, 1, 2, 5, 13, 32, 72, 148, 281, 499, 838, 1343, 2069, 3082, 4460, 6294, 8689, 11765, 15658, 20521, 26525, 33860, 42736, 53384, 66057, 81031, 98606, 119107, 142885, 170318, 201812, 237802, 278753, 325161, 377554, 436493, 502573, 576424, 658712, 750140, 851449 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..40.

M. D. Atkinson, Restricted permutations, Discrete Math., 195 (1999), 27-38.

Christian Bean, Bjarki Gudmundsson, Henning Ulfarsson, Automatic discovery of structural rules of permutation classes, arXiv:1705.04109 [math.CO], 2017.

J. West, Generating trees and forbidden subsequences, Discrete Math., 157 (1996), 363-374.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

a(n) = 1+binomial(n,2)+binomial(n+2,5).

G.f.: 1-x*(x^5-4*x^4+7*x^3-8*x^2+4*x-1)/(x-1)^6. - Colin Barker, Aug 02 2012

EXAMPLE

There are 13 permutations of length 4 which avoid these two patterns, so a(4)=13.

CROSSREFS

Cf. A116699, A116701, A116702, A088921, A005183, A116703, A001519.

Sequence in context: A082733 A095134 A086758 * A116702 A098156 A267862

Adjacent sequences:  A179254 A179255 A179256 * A179258 A179259 A179260

KEYWORD

nonn,easy

AUTHOR

Vincent Vatter, Jul 05 2010

EXTENSIONS

a(0)=1 prepended by Alois P. Heinz, Jul 05 2018

STATUS

approved

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Last modified August 6 09:02 EDT 2020. Contains 336228 sequences. (Running on oeis4.)