A184368 1/3 the number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having at least two equal elements connected horizontally or vertically.

21, 153, 1107, 8019, 58077, 420633, 3046491, 22064643, 159806277, 1157419449, 8382773187, 60713414163, 439725443661, 3184773389433, 23066169329547, 167059976482179, 1209955382858997, 8763272085493593, 63469230958692531

Offset: 1

Author

R. H. Hardin, Jan 12 2011

Keywords

• nonn

Comments

Column 1 of A184376.

Examples

			Some solutions for 3 X 2 with a(1,1)=0:
..0..0....0..0....0..1....0..0....0..0....0..1....0..1....0..2....0..1....0..0
..1..0....2..2....1..1....2..1....0..2....0..0....2..1....0..2....0..1....1..2
..2..0....1..1....2..0....0..0....0..2....0..2....2..2....0..2....0..2....1..0
		

Links

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

Crossrefs

Cf. A184376.

Formula

Empirical: a(n) = 6*a(n-1) + 9*a(n-2).

Conjectures from Colin Barker, Feb 27 2018: (Start)

G.f.: 3*x*(7 + 9*x) / (1 - 6*x - 9*x^2).

a(n) = ((3-3*sqrt(2))^n*(-4+3*sqrt(2)) + (3*(1+sqrt(2)))^n*(4+3*sqrt(2))) / (2*sqrt(2)).

(End)