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A116716 Number of permutations of length n which avoid the patterns 321, 2341, 4123. 2
1, 2, 5, 12, 26, 58, 131, 295, 662, 1487, 3342, 7510, 16874, 37915, 85195, 191432, 430143, 966522, 2171756, 4879892, 10965017, 24638169, 55361464, 124396081, 279515456, 628065528, 1411250432, 3171050937, 7125286777, 16010374058, 35974983957, 80835055196 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

David Lonoff and Jonah Ostroff, Symmetric Permutations Avoiding Two Patterns, Annals of Combinatorics 14 (1) pp.143-158 Springer, 2010; . - N. J. A. Sloane, Dec 27 2012

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (2,0,1,1,-1).

FORMULA

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

a(n) = 2*a(n-1) + a(n-3) + a(n-4) - a(n-5) for n>5. - Colin Barker, Oct 20 2017

PROG

(PARI) Vec(x*(1 + x)*(1 - x + 2*x^2 - x^3) / ((1 + x^2)*(1 - 2*x - x^2 + x^3)) + O(x^40)) \\ Colin Barker, Oct 20 2017

CROSSREFS

Sequence in context: A073778 A033490 A221950 * A128812 A241692 A078410

Adjacent sequences:  A116713 A116714 A116715 * A116717 A116718 A116719

KEYWORD

nonn,easy

AUTHOR

Lara Pudwell, Feb 26 2006

STATUS

approved

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Last modified July 2 08:50 EDT 2020. Contains 335398 sequences. (Running on oeis4.)