A226430 - OEIS

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A226430

The number of simple permutations of length n which avoid 1243 and 2431.

1

1, 2, 0, 2, 4, 10, 21, 44, 89, 178, 352, 692, 1355, 2648, 5171, 10100, 19744, 38646, 75761, 148772, 292653, 576678, 1138240, 2250152, 4454679, 8830640, 17525991, 34820264, 69244864, 137815978, 274487517, 547035452, 1090790465, 2176043098, 4342753696, 8669805020, 17313228899

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..37.

Jay Pantone, The Enumeration of Permutations Avoiding 3124 and 4312, arXiv:1309.0832 [math.CO], (2013)

Wikipedia, Permutation classes avoiding two patterns of length 4

Index entries for linear recurrences with constant coefficients, signature (4,-3,-4,3,2).

FORMULA

G.f.: (x-2*x^2-5*x^3+12*x^4+x^5-8*x^6-3*x^7)/((1-2*x)*(1-x-x^2)^2).

a(n) = -2*A000045(n+1) +A191830(n+2) +2^(n-3), n>2. - R. J. Mathar, Dec 06 2013

MATHEMATICA

Join[{1, 2}, LinearRecurrence[{4, -3, -4, 3, 2}, {0, 2, 4, 10, 21}, 40]] (* Jean-François Alcover, Jul 22 2018 *)

PROG

(PARI) x='x+O('x^66); Vec((x-2*x^2-5*x^3+12*x^4+x^5-8*x^6-3*x^7)/((1-2*x)*(1-x-x^2)^2)) \\ Joerg Arndt, Jun 19 2013

CROSSREFS

The number of all permutations which avoid 1243 and 2431 is A165534.

Sequence in context: A360860 A274414 A079550 * A067648 A279327 A052438

Adjacent sequences: A226427 A226428 A226429 * A226431 A226432 A226433

KEYWORD

nonn

AUTHOR

Jay Pantone, Jun 06 2013

STATUS

approved