A088921 -id:A088921 - cp's OEIS frontend

A119383 a(n) = n!- A088921(n).

0, 0, 0, 1, 11, 87, 640, 4855, 39909, 361995, 3626938, 39912947, 478993719, 6227004807, 87178258916, 1307674303055, 20922789757641, 355687427834707, 6402373705204718, 121645100407784603, 2432902008174544219

Offset: 0

Roger L. Bagula, Jun 07 2007

nonn

S. Billey, W. Jockusch and R. P. Stanley, Some combinatorial properties of Schubert polynomials, Journal of Algebraic Combinatorics 2(4) (1993) 345-374
S. Billey, W. Jockusch and R. P. Stanley. Some combinatorial properties of Schubert polynomials, Journal of Algebraic Combinatorics 2(4):345-374, 1993
K. Eriksson and S. Linusson, Combinatorics of Fulton's essential set, Duke Mathematical Journal 85(1) (1996) 61-76.
A. Vella, Pattern avoidance in permutations: linear and cyclic orders, Electron. J. Combin. 9 (2002/03), no. 2, #R18, 43 pp.

Cf. A088921.

g[n_] = n! - (2^(n + 1) - Binomial[n + 1, 3] - 2*n - 1); Table[g[n], {n, 0, 30}]

Offset set to 0, definition shortened, References converted to URL's - The Assoc. Eds. of the OEIS, Oct 20 2010

A179257 Number of permutations of length n which avoid the patterns 321 and 1324.

Original entry on oeis.org

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

Offset: 0

Vincent Vatter, Jul 05 2010

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

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).

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

LinearRecurrence[{6,-15,20,-15,6,-1},{1,1,2,5,13,32},50] (* Harvey P. Dale, May 19 2024 *)

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

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

cp's OEIS Frontend

A119383 a(n) = n!- A088921(n).

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