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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.
8
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
M. Albert, R. Aldred, M. Atkinson, C Handley, D. Holton, D. McCaughan and H. van Ditmarsch, Sorting Classes, Elec. J. of Comb., Vol. 12 (2005), R31.
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 *)
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
KEYWORD
nonn,easy
AUTHOR
Len Smiley, Nov 01 2005
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Mar 12 2024
STATUS
approved