A184145 1/4 the number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having at least two equal elements connected horizontally or vertically.

43, 499, 5695, 65227, 746503, 8544883, 97806031, 1119511003, 12814167895, 146673819139, 1678861073311, 19216616595691, 219957659413927, 2517684199404691, 28817972258232175, 329856907907420923

Offset

1,1

Comments

Column 1 of A184153.

Links

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

Formula

Empirical: a(n) = 9*a(n-1) + 28*a(n-2).

Conjectures from Colin Barker, Apr 12 2018: (Start)

G.f.: x*(43 + 112*x) / (1 - 9*x - 28*x^2).

a(n) = (2^(-n)*((9-sqrt(193))^n*(-25+2*sqrt(193)) + (9+sqrt(193))^n*(25+2*sqrt(193)))) / sqrt(193).

(End)

Example

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

Crossrefs

Cf. A184153.

Sequence in context: A188133 A194784 A184153 * A238202 A008388 A241939

Adjacent sequences: A184142 A184143 A184144 * A184146 A184147 A184148

Keyword

nonn

Author

R. H. Hardin, Jan 09 2011

Status

approved