A183690 Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock nonsingular.

50, 314, 1970, 12362, 77570, 486746, 3054290, 19165418, 120261410, 754630394, 4735243250, 29713259402, 186448243010, 1169947290266, 7341322395410, 46066190299178, 289061530659170, 1813837175689274, 11381678123719730

Offset

1,1

Comments

Column 1 of A183698.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) + 8*a(n-2).

Conjectures from Colin Barker, Apr 04 2018: (Start)

G.f.: 2*x*(25 + 32*x) / (1 - 5*x - 8*x^2).

a(n) = (2^(1-n)*((5-sqrt(57))^n*(-15+2*sqrt(57)) + (5+sqrt(57))^n*(15+2*sqrt(57)))) / sqrt(57).

(End)

Example

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

Crossrefs

Cf. A183698.

Sequence in context: A046656 A205620 A183698 * A221572 A124809 A261803

Adjacent sequences: A183687 A183688 A183689 * A183691 A183692 A183693

Keyword

nonn

Author

R. H. Hardin, Jan 06 2011

Status

approved