A207143 Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having nonzero determinant and commuting with every horizontal or vertical neighbor.

30, 48, 56, 95, 110, 187, 218, 371, 434, 740, 866, 1478, 1730, 2954, 3458, 5906, 6914, 11810, 13826, 23618, 27650, 47234, 55298, 94466, 110594, 188930, 221186, 377858, 442370, 755714, 884738, 1511426, 1769474, 3022850, 3538946, 6045698, 7077890

Offset

1,1

Comments

Column 2 of A207149.

Links

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

Formula

Empirical: a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) for n>9.

Empirical g.f.: x*(30 + 18*x - 52*x^2 + 3*x^3 - x^4 - x^5 + x^6 - x^7 + x^8) / ((1 - x)*(1 - 2*x^2)). - Colin Barker, Jun 19 2018

Example

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

Crossrefs

Cf. A207149.

Sequence in context: A075290 A281919 A004222 * A004223 A230558 A272949

Adjacent sequences: A207140 A207141 A207142 * A207144 A207145 A207146

Keyword

nonn

Author

R. H. Hardin, Feb 15 2012

Status

approved