A208104 Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 1 1 and 1 1 0 vertically.

9, 81, 169, 361, 841, 2025, 5041, 12769, 32761, 84681, 219961, 573049, 1495729, 3908529, 10220809, 26739241, 69973225, 183142089, 479391025, 1254930625, 3285238489, 8600522121, 22515902809, 58946498521, 154322479921, 404019140625

Offset: 1

Author

R. H. Hardin, Feb 23 2012

Keywords

• nonn

Comments

Column 4 of A208108.

Examples

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

Links

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

Crossrefs

Cf. A208108.

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*(9 + 45*x - 137*x^2 - 99*x^3 + 185*x^4 + 55*x^5 - 40*x^6) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)*(1 - x - x^2)). - Colin Barker, Jun 28 2018