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

1,2

Comments

Row 2 of A189449.

Links

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

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)

Example

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

Crossrefs

Cf. A189449.

Sequence in context: A203232 A098347 A203414 * A180719 A343164 A300317

Adjacent sequences: A189447 A189448 A189449 * A189451 A189452 A189453

Keyword

nonn

Author

R. H. Hardin, Apr 22 2011

Status

approved