A189348 Number of n X 2 array permutations with each element moving one space diagonally, horizontally or vertically.

1, 4, 13, 45, 160, 565, 2005, 7108, 25209, 89401, 317056, 1124425, 3987721, 14142276, 50154949, 177872293, 630816160, 2237161405, 7933993245, 28137553540, 99788579953, 353895752689, 1255075518976, 4451069407761, 15785519335825

Offset: 1

Author

R. H. Hardin, Apr 20 2011

Keywords

• nonn

Comments

Column 2 of A189355.

Examples

			Some solutions for 3 X 2:
..1..3....2..0....3..0....1..0....1..0....3..0....1..0....1..3....1..3....1..0
..0..5....3..1....5..1....4..5....3..5....4..1....4..2....5..0....0..2....3..2
..2..4....5..4....2..4....2..3....2..4....5..2....5..3....2..4....5..4....5..4
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A189355.

Formula

Empirical: a(n) = 3*a(n-1) +3*a(n-2) -3*a(n-3) -3*a(n-4) +a(n-5).

Empirical g.f.: x*(1 + x - 2*x^2 - 3*x^3 + x^4) / ((1 - x)*(1 - 2*x - 5*x^2 - 2*x^3 + x^4)). - Colin Barker, May 02 2018