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A116718 Number of permutations of length n which avoid the patterns 321, 1342, 3124. 0
1, 1, 2, 5, 12, 22, 37, 60, 96, 153, 244, 390, 625, 1004, 1616, 2605, 4204, 6790, 10973, 17740, 28688, 46401, 75060, 121430, 196457, 317852, 514272, 832085, 1346316, 2178358, 3524629, 5702940, 9227520, 14930409, 24157876, 39088230, 63246049, 102334220 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

It appears that, for n > 2, a(n) = F(n+3) + 2*n - 9, where F is A000045. - Jason Kimberley, Nov 22 2013

LINKS

Table of n, a(n) for n=0..37.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (3, -2, -1, 1).

FORMULA

G.f.: 1+(x+1)*(2*x^4+x^3-3*x^2+2*x-1)*x/((x-1)^2*(x^2+x-1)).

a(0)=1, a(1)=1, a(2)=2, a(3)=5, a(4)=12, a(5)=22, a(6)=37, a(n)=3*a(n-1)- 2*a(n-2)- a(n-3)+a (n-4). - Harvey P. Dale, Oct 21 2011

For n>2, a(n) = (1+2/sqrt(5))*((1+sqrt(5))/2)^n + (1-2/sqrt(5))*((1-sqrt(5))/2)^n + 2*n - 9. - Vaclav Kotesovec, Dec 11 2013

MATHEMATICA

Rest[CoefficientList[Series[1+((x+1)(2x^4+x^3-3x^2+2x-1)x)/((x-1)^2 (x^2+ x-1)), {x, 0, 50}], x]] (* or *) Join[{1, 1, 2}, LinearRecurrence[{3, -2, -1, 1}, {5, 12, 22, 37}, 50]] (* Harvey P. Dale, Oct 21 2011 *)

CROSSREFS

Sequence in context: A116727 A116729 A048840 * A026035 A215183 A086734

Adjacent sequences:  A116715 A116716 A116717 * A116719 A116720 A116721

KEYWORD

nonn,easy

AUTHOR

Lara Pudwell, Feb 26 2006

STATUS

approved

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Last modified July 10 14:17 EDT 2020. Contains 335576 sequences. (Running on oeis4.)