A183245 Number of permutations of 1..2*n+2 with each element displaced by at least n.

9, 29, 112, 436, 1708, 6724, 26572, 105316, 418348, 1664644, 6632332, 26450596, 105566188, 421556164, 1684098892, 6730018276, 26900941228, 107546369284, 430013290252, 1719536600356, 6876596719468, 27501737832004, 109993004190412

Offset: 1

Author

R. H. Hardin, Jan 03 2011

Keywords

• nonn

Comments

Row 3 of A183244.

Examples

			All permutations of 1-6 with minimum displacement 2:
(4,5,1,6,2,3) (4,5,1,6,3,2) (4,5,6,1,2,3) (4,5,6,1,3,2) (4,5,6,2,1,3)
(4,5,6,2,3,1) (4,6,5,1,2,3) (4,6,5,1,3,2) (4,6,5,2,1,3) (4,6,5,2,3,1)
(5,4,1,6,2,3) (5,4,1,6,3,2) (5,4,6,1,2,3) (5,4,6,1,3,2) (5,4,6,2,1,3)
(5,4,6,2,3,1) (5,6,1,2,3,4) (3,4,5,6,1,2) (3,4,5,6,2,1) (3,5,1,6,2,4)
(3,5,6,1,2,4) (3,5,6,2,1,4) (3,6,5,1,2,4) (3,6,5,2,1,4) (6,4,5,1,2,3)
(6,4,5,1,3,2) (6,4,5,2,1,3) (6,4,5,2,3,1) (6,5,1,2,3,4)
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..131

Crossrefs

Cf. A183244.

Formula

Empirical (for n>=2): 25*4^(n-2) + 4*3^(n-2). - Vaclav Kotesovec, Nov 27 2012

Conjectures from Colin Barker, Mar 27 2018: (Start)

G.f.: x*(9 - 34*x + 17*x^2) / ((1 - 3*x)*(1 - 4*x)).

a(n) = 7*a(n-1) - 12*a(n-2) for n>3.

(End)