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

1,1

Comments

Row 3 of A183244.

Links

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

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)

Example

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)

Crossrefs

Cf. A183244.

Sequence in context: A147376 A201447 A288744 * A101141 A056258 A147282

Adjacent sequences: A183242 A183243 A183244 * A183246 A183247 A183248

Keyword

nonn

Author

R. H. Hardin, Jan 03 2011

Status

approved