A207148 Number of (n+1) X 8 0..2 arrays with every 2 X 2 subblock having nonzero determinant and commuting with every horizontal or vertical neighbor.

315, 218, 619, 434, 1238, 866, 2482, 1730, 4946, 3458, 9874, 6914, 19730, 13826, 39458, 27650, 78914, 55298, 157826, 110594, 315650, 221186, 631298, 442370, 1262594, 884738, 2525186, 1769474, 5050370, 3538946, 10100738, 7077890

Offset

1,1

Comments

Column 7 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>14.

Empirical g.f.: x*(315 - 97*x - 229*x^2 + 9*x^3 + 2*x^4 - 2*x^5 + 8*x^6 - 8*x^7 - 16*x^8 + 16*x^9 - 16*x^10 + 16*x^11 - 16*x^12 + 16*x^13) / ((1 - x)*(1 - 2*x^2)). - Colin Barker, Jun 19 2018

Example

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

Crossrefs

Cf. A207149.

Sequence in context: A231021 A104819 A283901 * A361034 A210889 A210891

Adjacent sequences: A207145 A207146 A207147 * A207149 A207150 A207151

Keyword

nonn

Author

R. H. Hardin, Feb 15 2012

Status

approved