A189450 Number of 2 X n array permutations with each element moving zero or one space horizontally or diagonally.

1, 5, 16, 61, 225, 841, 3136, 11705, 43681, 163021, 608400, 2270581, 8473921, 31625105, 118026496, 440480881, 1643897025, 6135107221, 22896531856, 85451020205, 318907548961, 1190179175641, 4441809153600, 16577057438761

Offset: 1

Author

R. H. Hardin, Apr 22 2011

Keywords

• nonn

Comments

Row 2 of A189449.

Examples

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

Links

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

Crossrefs

Cf. A189449.

Formula

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

Conjectures from Colin Barker, May 02 2018: (Start)

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

a(n) = ((2-sqrt(3))^(n+1) + (2+sqrt(3))^(n+1) + 8) / 12 for n even.

a(n) = (-2+(2-sqrt(3))^(1+n) + (2+sqrt(3))^(1+n)) / 12 for n odd.

(End)