A223381 Number of n X 2 0..2 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..2 introduced in row major order.

2, 9, 57, 366, 2358, 15204, 98052, 632376, 4078488, 26304144, 169648272, 1094144736, 7056675168, 45511953984, 293528880192, 1893111501696, 12209603211648, 78745710676224, 507869653293312, 3275500119584256

Offset

1,1

Comments

Column 2 of A223387.

Links

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

Formula

Empirical: a(n) = 8*a(n-1) - 10*a(n-2) for n>3.

Conjectures from Colin Barker, Aug 20 2018: (Start)

G.f.: x*(1 - x)*(2 - 5*x) / (1 - 8*x + 10*x^2).

a(n) = (-(4-sqrt(6))^n*(-6+sqrt(6)) + (4+sqrt(6))^n*(6+sqrt(6))) / 40 for n>1.

(End)

Example

Some solutions for n=3:
..0..1....0..1....0..0....0..0....0..1....0..1....0..1....0..1....0..1....0..1
..2..0....2..1....1..2....1..1....0..2....0..2....2..0....2..0....0..2....0..1
..0..2....0..2....0..2....0..2....2..0....0..1....1..1....2..1....1..0....0..1

Crossrefs

Cf. A223387.

Sequence in context: A371196 A004103 A295775 * A175896 A175900 A175912

Adjacent sequences: A223378 A223379 A223380 * A223382 A223383 A223384

Keyword

nonn

Author

R. H. Hardin, Mar 19 2013

Status

approved