The On-Line Encyclopedia of Integer Sequences (OEIS)

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A116711

Number of permutations of length n which avoid the patterns 123, 3214, 4312.
(history; published version)

#12 by N. J. A. Sloane at Mon Oct 23 19:56:31 EDT 2017

STATUS

reviewed

approved

#11 by Michel Marcus at Mon Oct 23 14:57:10 EDT 2017

STATUS

proposed

reviewed

#10 by Colin Barker at Mon Oct 23 14:25:54 EDT 2017

STATUS

editing

proposed

#9 by Colin Barker at Mon Oct 23 14:25:23 EDT 2017

LINKS

Colin Barker, <a href="/A116711/b116711.txt">Table of n, a(n) for n = 1..1000</a>

<a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

FORMULA

G.f.: A(x) = *(1 - x*( + 2*x^5-2 + 2*x^3 - 2*x^2+x-5) / (1) / ( - x-1)^3.

For n >= 4, a(n) = n^2 + 2n 2*n - 12. - Franklin T. Adams-Watters, Sep 16 2006

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3. - Colin Barker, Oct 23 2017

PROG

(PARI) Vec(x*(1 - x + 2*x^2 + 2*x^3 - 2*x^5) / (1 - x)^3 + O(x^50)) \\ Colin Barker, Oct 23 2017

STATUS

approved

editing

#8 by Alois P. Heinz at Mon Jan 11 11:08:43 EST 2016

STATUS

editing

approved

#7 by Alois P. Heinz at Mon Jan 11 11:08:20 EST 2016

DATA

1, 2, 5, 12, 23, 36, 51, 68, 87, 108, 131, 156, 183, 212, 243, 276, 311, 348, 387, 428, 471, 516, 563, 612, 663, 716, 771, 828, 887, 948, 1011, 1076, 1143, 1212, 1283, 1356, 1431, 1508, 1587, 1668, 1751, 1836, 1923, 2012, 2103, 2196, 2291, 2388, 2487, 2588

FORMULA

G.f.: A(x) = {x*(2x2*x^5-2x2*x^3-2x2*x^2+x-1)} /{ (x-1)^3}.

For n >= 4, a(n) = n^2 + 2n - 12. - _Franklin T. Adams-Watters, _, Sep 16 2006

STATUS

approved

editing

#6 by N. J. A. Sloane at Mon Oct 05 11:30:42 EDT 2015

LINKS

Lara Pudwell, <a href="http://www.mathfaculty.rutgersvalpo.edu/~lpudwell/maple/webbook/bookmain.html">Systematic Studies in Pattern Avoidance</a>, 2005.

Discussion

Mon Oct 05

11:30

OEIS Server: https://oeis.org/edit/global/2462

#5 by Russ Cox at Sat Mar 31 10:32:21 EDT 2012

AUTHOR

Lara Pudwell (_Lara. Pudwell(AT)valpo.edu), _, Feb 26 2006

Discussion

Sat Mar 31

10:32

OEIS Server: https://oeis.org/edit/global/775

#4 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

KEYWORD

nonn,easy,new

AUTHOR

Lara Pudwell (lpudwellLara.Pudwell(AT)math.rutgersvalpo.edu), Feb 26 2006

#3 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008

KEYWORD

nonn,easy,new

AUTHOR

Lara Pudwell (lpudwell(AT)math.rutgers.edu), Feb 26 2006