A111286 Number of permutations avoiding the patterns {1342, 1432, 2341, 2431, 3142, 3241, 3412, 3421, 4132, 4231, 4312, 4321}; number of strong sorting class based on 1342.

1, 1, 2, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786432, 1572864, 3145728, 6291456, 12582912, 25165824, 50331648, 100663296, 201326592, 402653184, 805306368, 1610612736, 3221225472

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

M. H. Albert, R. E. L. Aldred, M. D. Atkinson, C. C. Handley, D. A. Holton, D. J. McCaughan, and H. van Ditmarsch, Sorting Classes, Elec. J. of Comb., Vol. 12 (2005), R31.

Index entries for linear recurrences with constant coefficients, signature (2).

Formula

a(n) = 3*2^(n-2), n>=3.

a(n) = 2*a(n-1) for n=3. G.f.: (1-x+2*x^3)/(1-2*x). - Colin Barker, Nov 29 2012

Mathematica

Table[If[n == 1, 1, If[n == 2, 2, 3*2^(n - 2)]], {n, 32}] (* Robert G. Wilson v, Nov 04 2005 *)
LinearRecurrence[{2}, {1, 2, 6}, 40] (* Harvey P. Dale, Jul 14 2019 *)

Crossrefs

Cf. A003945, A007283, A042950, A098011, A110164 - differs from each by one initial term.

Sequence in context: A003680 A337257 A051487 * A058295 A309841 A132176

Adjacent sequences: A111283 A111284 A111285 * A111287 A111288 A111289

Keyword

nonn,easy

Author

Len Smiley, Nov 01 2005

Extensions

a(0)=1 prepended by Alois P. Heinz, Mar 12 2024

Status

approved