A183702 Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock nonsingular.

192, 2472, 31800, 409128, 5263608, 67718760, 871232952, 11208812712, 144206530680, 1855283342568, 23869073504568, 307086608771880, 3950810460600312, 50828993677128552, 653938381502821560

Offset

1,1

Comments

Column 1 of A183710.

Links

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

Formula

Empirical: a(n) = 11*a(n-1) + 24*a(n-2).

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

G.f.: 24*x*(8 + 15*x) / (1 - 11*x - 24*x^2).

a(n) = (3*2^(-1-n)*((11-sqrt(217))^n*(-73+5*sqrt(217)) + (11+sqrt(217))^n*(73+5*sqrt(217)))) / sqrt(217).

(End)

Example

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

Crossrefs

Cf. A183710.

Sequence in context: A251442 A251435 A183710 * A351632 A174384 A232919

Adjacent sequences: A183699 A183700 A183701 * A183703 A183704 A183705

Keyword

nonn

Author

R. H. Hardin, Jan 06 2011

Status

approved