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A116720 Number of permutations of length n which avoid the patterns 213, 1234, 4312. 1
1, 2, 5, 12, 25, 44, 69, 100, 137, 180, 229, 284, 345, 412, 485, 564, 649, 740, 837, 940, 1049, 1164, 1285, 1412, 1545, 1684, 1829, 1980, 2137, 2300, 2469, 2644, 2825, 3012, 3205, 3404, 3609, 3820, 4037, 4260, 4489, 4724, 4965, 5212, 5465, 5724, 5989, 6260 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..48.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

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

FORMULA

G.f.: A(x) = -{x(2x^4+2x^3+2x^2-x+1)}/{(x-1)^3}

For n >= 3, a(n) = 3n^2 - 14n + 20. - Franklin T. Adams-Watters, Sep 16 2006

MAPLE

A116720 := proc(n) coeftayl(-x*(2*x^4+2*x^3+2*x^2-x+1)/(x-1)^3, x=0, n) ; end: seq(A116720(n), n=1..60) ; # R. J. Mathar, Jan 23 2008

MATHEMATICA

f[n_]:=n+(n+1)*(n+2)+(n+3)*(n+4)+(n+5)*(n+6); lst={1, 2}; Do[AppendTo[lst, f[n]], {n, -3, 5!}]; lst [Vladimir Joseph Stephan Orlovsky, Oct 08 2009]

LinearRecurrence[{3, -3, 1}, {1, 2, 5, 12, 25}, 50] (* Harvey P. Dale, May 06 2017 *)

CROSSREFS

Sequence in context: A322779 A096584 A002836 * A116731 A116722 A116730

Adjacent sequences:  A116717 A116718 A116719 * A116721 A116722 A116723

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 15 23:32 EDT 2020. Contains 335774 sequences. (Running on oeis4.)