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A231228 Number of permutations of [n] with exactly one occurrence of one of the consecutive patterns 123, 1432, 2431, 3421. 2
0, 0, 0, 1, 9, 59, 358, 2235, 14658, 103270, 778451, 6315499, 54733657, 507655301, 5003179539, 52430810493, 580611272956, 6796733911852, 83658527086447, 1083027034959367, 14678725047527255, 208344799726820123, 3084495765476262875, 47646333262275943521 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

FORMULA

a(n) ~ c * (2/Pi)^n * n! * n, where c = 3.08472832460941829086964816782... . - Vaclav Kotesovec, Aug 28 2014

EXAMPLE

a(3) = 1: 123.

a(4) = 9: 1243, 1342, 1432, 2134, 2341, 2431, 3124, 3421, 4123.

a(5) = 59: 12435, 12534, 13245, ..., 53124, 53421, 54123.

a(6) = 358: 124365, 125364, 125463, ..., 653124, 653421, 654123.

MAPLE

b:= proc(u, o, t) option remember;

      `if`(t=7, 0, `if`(u+o=0, `if`(t in [4, 5, 6], 1, 0),

      add(b(u+j-1, o-j, [2, 5, 2, 5, 7, 5][t]), j=1..o)+

      add(b(u-j, o+j-1, [1, 3, 4, 4, 6, 7][t]), j=1..u)))

    end:

a:= n-> b(n, 0, 1):

seq(a(n), n=0..25);

CROSSREFS

Column k=1 of A231210.

Sequence in context: A174654 A027249 A026717 * A198847 A059356 A039929

Adjacent sequences:  A231225 A231226 A231227 * A231229 A231230 A231231

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 05 2013

STATUS

approved

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Last modified January 22 19:16 EST 2020. Contains 331153 sequences. (Running on oeis4.)