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A116721 Number of permutations of length n which avoid the patterns 123, 3142, 4312; or avoid the patterns 123, 3421, 4231. 1
1, 2, 5, 12, 24, 42, 67, 100, 142, 194, 257, 332, 420, 522, 639, 772, 922, 1090, 1277, 1484, 1712, 1962, 2235, 2532, 2854, 3202, 3577, 3980, 4412, 4874, 5367, 5892, 6450, 7042, 7669, 8332, 9032, 9770, 10547, 11364, 12222, 13122, 14065, 15052, 16084, 17162 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

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

For n >= 2, a(n) = (n^3 + 3n^2 - 16n + 24)/6. - Franklin T. Adams-Watters, Sep 16 2006

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5. - Colin Barker, Oct 24 2017

MAPLE

A116721 := proc(n) coeftayl(-x*(x^4-3*x^2+2*x-1)/(x-1)^4, x=0, n) ; end: seq(A116721(n), n=1..60) ; # R. J. Mathar, Jan 23 2008

PROG

(PARI) Vec(x*(1 - 2*x + 3*x^2 - x^4) / (1 - x)^4 + O(x^100)) \\ Colin Barker, Oct 24 2017

CROSSREFS

Sequence in context: A112287 A127787 A116733 * A294868 A192981 A116713

Adjacent sequences:  A116718 A116719 A116720 * A116722 A116723 A116724

KEYWORD

nonn,easy

AUTHOR

Lara Pudwell, Feb 26 2006

EXTENSIONS

More terms from R. J. Mathar, Jan 23 2008

STATUS

approved

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Last modified July 12 21:31 EDT 2020. Contains 335669 sequences. (Running on oeis4.)