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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
OFFSET
1,2
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 A368638
KEYWORD
nonn,easy
AUTHOR
Lara Pudwell, Feb 26 2006
EXTENSIONS
More terms from R. J. Mathar, Jan 23 2008
STATUS
approved