A203969 Number of n X 2 0..2 arrays with every 1 immediately preceded by 0 to the left or above, and every 2 immediately preceded by 0 1 to the left or above.

2, 7, 29, 106, 396, 1488, 5569, 20859, 78133, 292644, 1096125, 4105590, 15377699, 57598086, 215736791, 808054127, 3026612006, 11336343903, 42460908170, 159039700345, 595692067467, 2231197862121, 8357076036219, 31301894398172

Offset: 1

Author

R. H. Hardin, Jan 08 2012

Keywords

• nonn

Comments

Column 2 of A203975.

Examples

			Some solutions for n=5:
..0..1....0..1....0..1....0..1....0..0....0..0....0..0....0..0....0..0....0..0
..0..1....1..0....0..0....0..1....1..1....0..0....0..1....1..0....0..1....1..1
..0..0....0..1....0..1....1..0....0..1....0..1....1..2....2..1....0..1....0..0
..0..1....0..2....1..0....2..0....0..1....0..1....0..0....0..0....0..0....0..0
..0..0....0..1....2..0....0..0....1..0....0..1....0..0....0..1....1..1....1..1
		

Links

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

Crossrefs

Cf. A203975.

Formula

Empirical: a(n) = 2*a(n-1) +3*a(n-2) +12*a(n-3) +4*a(n-4) +5*a(n-5) -9*a(n-6) -a(n-8) +a(n-9).

Empirical g.f.: x*(2 + 3*x + 9*x^2 + 3*x^3 + 5*x^4 - 8*x^5 - x^7 + x^8) / ((1 + x + x^2 - x^3)*(1 - 3*x - x^2 - 7*x^3 + x^4 + x^6)). - Colin Barker, Jun 06 2018