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

1,1

Comments

Column 1 of A184376.

Links

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

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)

Example

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

Crossrefs

Cf. A184376.

Sequence in context: A221694 A229262 A184376 * A078396 A301883 A302080

Adjacent sequences: A184365 A184366 A184367 * A184369 A184370 A184371

Keyword

nonn

Author

R. H. Hardin, Jan 12 2011

Status

approved