A116823 Number of permutations of length n which avoid the patterns 1342, 3142, 4312; or avoid the patterns 3124, 3412, 3421.

1, 2, 6, 21, 75, 266, 935, 3263, 11326, 39155, 134955, 464094, 1593231, 5462447, 18709694, 64035275, 219039523, 748919582, 2559777591, 8746974087, 29883271518, 102078226067, 348648695387, 1190706243710, 4066228992799

Offset

1,2

Links

Harvey P. Dale, 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 (7,-15,10,-2).

Formula

G.f.: A(x) = -{(x^3-7x^2+5x-1)x}/{(2x^2-4x+1)(x^2-3x+1)}

Mathematica

LinearRecurrence[{7, -15, 10, -2}, {1, 2, 6, 21}, 30] (* Harvey P. Dale, Jul 06 2021 *)

Crossrefs

Sequence in context: A369626 A294815 A116751 * A289597 A116743 A294816

Adjacent sequences: A116820 A116821 A116822 * A116824 A116825 A116826

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved