A188701 Number of n X 4 binary arrays without the pattern 0 0 diagonally or vertically.

16, 55, 387, 1876, 10857, 57665, 318732, 1729531, 9464035, 51591068, 281717653, 1537169293, 8390298820, 45789639603, 249911548135, 1363931051824, 7443964229917, 40626890315469, 221729775973184, 1210135365944631

Offset: 1

Author

R. H. Hardin, Apr 08 2011

Keywords

• nonn

Comments

Column 4 of A188706.

Examples

			Some solutions for 3 X 4:
..0..0..1..0....1..1..0..0....1..1..0..1....1..1..1..1....1..1..0..0
..1..1..1..1....1..1..1..1....1..0..1..1....1..1..1..0....0..1..1..1
..0..0..0..0....0..1..1..0....1..1..1..1....0..1..1..1....1..1..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A188706.

Formula

Empirical: a(n) = a(n-1) + 20*a(n-2) + 27*a(n-3) - 14*a(n-4) - 25*a(n-5) + 4*a(n-6) + 5*a(n-7) - a(n-8).

Empirical g.f.: x*(16 + 39*x + 12*x^2 - 43*x^3 - 20*x^4 + 9*x^5 + 4*x^6 - x^7) / ((1 + x)*(1 + 2*x - x^2)*(1 - 4*x - 9*x^2 + 5*x^3 + 4*x^4 - x^5)). - Colin Barker, Apr 28 2018