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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
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.
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
a(n) = 1+A027658(n-2). - R. J. Mathar, Aug 19 2022
EXAMPLE
There are 13 permutations of length 4 which avoid these two patterns, so a(4)=13.
CROSSREFS
Sequence in context: A082733 A095134 A086758 * A116702 A098156 A267862
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 March 29 05:43 EDT 2024. Contains 371264 sequences. (Running on oeis4.)