A208103 Number of n X 3 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 1 1 and 1 1 0 vertically.

6, 36, 78, 171, 406, 990, 2485, 6328, 16290, 42195, 109746, 286146, 747253, 1953276, 5108806, 13367035, 34982430, 91564278, 239684565, 627447600, 1642590586, 4300214691, 11257876378, 29473127866, 77161043541, 202009252500

Offset

1,1

Comments

Column 3 of A208108.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 6*a(n-3) + 4*a(n-4) + 2*a(n-5) - a(n-6) for n>7.

Empirical g.f.: x*(6 + 12*x - 54*x^2 - 33*x^3 + 70*x^4 + 20*x^5 - 15*x^6) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)*(1 - x - x^2)). - Colin Barker, Mar 06 2018

Example

Some solutions for n=10:
..1..0..0....0..0..1....1..0..0....0..1..1....0..1..1....0..0..1....1..0..1
..0..0..1....1..0..0....0..0..1....0..0..1....0..0..1....0..1..1....1..0..1
..1..0..0....0..1..1....1..1..0....0..0..1....1..0..1....0..0..1....1..0..1
..0..1..1....1..0..0....0..0..1....0..1..1....0..1..1....1..1..1....1..0..1
..1..0..0....0..1..1....1..0..0....0..0..1....1..0..1....0..0..1....1..1..1
..0..1..1....1..0..0....0..0..1....0..0..1....0..0..1....0..1..1....1..0..1
..1..0..0....0..0..1....1..0..0....0..1..1....1..0..1....1..0..1....1..1..1
..0..0..1....1..0..0....0..0..1....1..0..1....0..0..1....0..1..1....1..0..1
..1..1..0....0..1..1....1..0..0....0..0..1....0..1..1....1..0..1....1..0..1
..0..0..1....1..0..0....0..0..1....0..0..1....0..0..1....0..1..1....1..0..1

Crossrefs

Cf. A208108.

Sequence in context: A043116 A044108 A207730 * A207724 A208689 A207483

Adjacent sequences: A208100 A208101 A208102 * A208104 A208105 A208106

Keyword

nonn

Author

R. H. Hardin, Feb 23 2012

Status

approved