A258216 Number of permutations of {1,2,3,...,n} such that no multiples of 3 are adjacent.

1, 1, 2, 6, 24, 120, 480, 3600, 30240, 151200, 1693440, 20321280, 121927680, 1828915200, 28740096000, 201180672000, 3793692672000, 73977007104000, 591816056832000, 13463815292928000, 314155690168320000

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = factorial(n-floor(n/3))*fallfac(n+1-floor(n/3),floor(n/3)), where fallfac is falling factorial, A008279.

a(n) ~ n! * 2^(2*n+2-2*floor(n,3)/3) / 3^(n+1/2). - Vaclav Kotesovec, May 23 2015

Mathematica

Table[Factorial[n-Floor[n/3]]*FactorialPower[n+1-Floor[n/3], Floor[n/3], 1], {n, 0, 20}]

Crossrefs

Cf. A008279, A010790, A258213.

Sequence in context: A174701 A178848 A173845 * A263748 A072856 A228401

Adjacent sequences: A258213 A258214 A258215 * A258217 A258218 A258219

Keyword

nonn,easy

Author

Ran Pan, May 23 2015

Status

approved