A269889 The number of permutations of 1, 2,..., n such that none of 123, 132, 213, 231, 312, 321 appear in the permutation.

1, 1, 2, 0, 12, 84, 576, 4320, 36000, 332640, 3386880, 37739520, 457228800, 5987520000, 84304281600, 1270312243200, 20399720140800, 347841381888000, 6276836966400000, 119510975840256000, 2394487765942272000, 50361071569256448000, 1109403315728547840000

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

a(n) = n! - 6(n-2)! for n>=3.

-(n+1)*(n-4)*a(n) +(n-2)*(n-3)*(n+2)*a(n-1)=0 for n>=4 - R. J. Mathar, Nov 07 2017

Example

There are 12 ways that permutations of 4 can have 1, 2, and 3 together.  They are: 1234, 1324, 2134, 2314, 3124, 3214, 4123, 4132, 4213, 4231, 4312, 4321. Since there are 24 permutations, a(4) = 24-12 = 12

Mathematica

Table[If[n < 3, n!, n! - 6 (n - 2)!], {n, 0, 22}] (* Michael De Vlieger, Mar 07 2016 *)

Crossrefs

Cf. A000142.

Sequence in context: A013316 A353222 A013310 * A293567 A293494 A058803

Adjacent sequences: A269886 A269887 A269888 * A269890 A269891 A269892

Keyword

nonn

Author

Chris Wu, Mar 07 2016

Status

approved