A206338 Number of (n+1) X 4 0..3 arrays with every 2 X 2 subblock having nonzero determinant and commuting with every horizontal or vertical neighbor.

455, 232, 1340, 682, 4007, 2030, 12005, 6074, 35999, 18206, 107983, 54606, 323937, 163806, 971799, 491406, 2915385, 1474206, 8746143, 4422606, 26238417, 13267806, 78715239, 39803406, 236145705, 119410206, 708437103, 358230606, 2125311297

Offset

1,1

Comments

Column 3 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>12.

Empirical g.f.: x*(455 - 223*x - 257*x^2 + 11*x^3 + x^4 - 3*x^5 + 2*x^10 + 2*x^11) / ((1 - x)*(1 - 3*x^2)). - Colin Barker, Jun 15 2018

Example

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

Crossrefs

Cf. A206343.

Sequence in context: A092267 A232758 A284430 * A123563 A043475 A324633

Adjacent sequences: A206335 A206336 A206337 * A206339 A206340 A206341

Keyword

nonn

Author

R. H. Hardin, Feb 06 2012

Status

approved