A184031 1/16 the number of (n+1) X 2 0..3 arrays with all 2 X 2 subblocks having the same four values.

16, 28, 49, 91, 169, 325, 625, 1225, 2401, 4753, 9409, 18721, 37249, 74305, 148225, 296065, 591361, 1181953, 2362369, 4723201, 9443329, 18883585, 37761025, 75515905, 151019521, 302026753, 604028929, 1208033281, 2416017409, 4831985665

Offset: 1

Author

R. H. Hardin, Jan 08 2011

Keywords

• nonn

Comments

Column 1 of A184039.

Examples

			Some solutions for 3 X 2:
..1..2....2..1....2..0....0..1....1..2....0..2....2..2....1..0....1..0....1..3
..1..0....3..3....1..0....0..2....2..2....3..2....1..1....1..3....0..0....3..2
..2..1....2..1....0..2....0..1....1..2....0..2....2..2....1..0....0..1....1..3
		

Links

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

Crossrefs

Cf. A184039.

Formula

Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).

Conjectures from Colin Barker, Apr 10 2018: (Start)

G.f.: x*(16 - 20*x - 35*x^2 + 40*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

a(n) = 9*2^(n/2-1) + 9*2^(n-1) + 1 for n even.

a(n) = 9*2^(n-1) + 3*2^((n+1)/2) + 1 for n odd.

(End)