A206337 Number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock having nonzero determinant and commuting with every horizontal or vertical neighbor.

96, 181, 232, 534, 686, 1589, 2042, 4751, 6110, 14239, 18318, 42705, 54942, 128103, 164814, 384297, 494430, 1152879, 1483278, 3458625, 4449822, 10375863, 13349454, 31127577, 40048350, 93382719, 120145038, 280148145, 360435102, 840444423

Offset

1,1

Comments

Column 2 of A206343.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) for n>11.

Empirical g.f.: x*(96 + 85*x - 237*x^2 + 47*x^3 - x^4 - 3*x^5 - 3*x^6 + 2*x^9 + 2*x^10) / ((1 - x)*(1 - 3*x^2)). - Colin Barker, Jun 15 2018

Example

Some solutions for n=4:
..3..0..1....0..1..0....1..3..1....0..2..0....0..1..0....1..0..1....0..1..0
..0..3..0....3..0..1....3..1..3....3..0..2....1..0..1....0..1..0....3..0..1
..2..0..3....0..3..0....1..3..1....0..3..0....0..1..0....2..0..1....0..3..0
..0..2..0....1..0..3....3..1..3....1..0..3....2..0..1....0..2..0....3..0..3
..1..0..2....0..1..0....1..3..1....0..1..3....0..2..1....1..0..2....0..3..3

Crossrefs

Cf. A206343.

Sequence in context: A143847 A178740 A090762 * A161482 A352975 A044428

Adjacent sequences: A206334 A206335 A206336 * A206338 A206339 A206340

Keyword

nonn

Author

R. H. Hardin, Feb 06 2012

Status

approved