A183246 Number of permutations of 1..2*n+3 with each element displaced by at least n.

44, 206, 1168, 6984, 41808, 250464, 1501248, 9001344, 53983488, 323802624, 1942422528, 11652962304, 69911482368, 419443728384, 2516561707008, 15098967588864, 90592194920448, 543546727071744, 3261254592626688

Offset: 1

Author

R. H. Hardin, Jan 03 2011

Keywords

• nonn

Comments

Row 4 of A183244.

Examples

			Some permutations of 1-7 with minimum displacement 2:
(4,5,6,1,7,3,2) (3,6,5,7,2,4,1) (7,6,1,2,3,4,5) (6,4,1,2,7,3,5) (5,6,7,1,3,2,4)
(3,7,5,6,1,4,2) (5,6,1,2,7,3,4) (6,5,7,2,1,4,3) (6,5,1,7,3,4,2) (6,5,1,7,2,4,3)
(7,5,6,1,2,3,4) (5,7,1,6,2,3,4) (3,4,6,7,1,2,5) (4,6,5,7,2,1,3) (7,4,5,6,1,2,3)
(6,4,7,2,1,3,5) (4,6,1,7,3,2,5) (5,6,1,2,7,4,3) (5,4,6,7,1,3,2) (3,5,7,6,2,1,4)
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..66

Crossrefs

Cf. A183244.

Formula

Empirical (for n>=3): 289/9*6^(n-1) + 3*4^(n-2). - Vaclav Kotesovec, Nov 27 2012

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

G.f.: 2*x*(22 - 117*x + 82*x^2 + 124*x^3) / ((1 - 4*x)*(1 - 6*x)).

a(n) = 10*a(n-1) - 24*a(n-2) for n>4.

(End)