A231057 Number of n X 2 0..3 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.

0, 2, 6, 20, 68, 230, 778, 2632, 8904, 30122, 101902, 344732, 1166220, 3945294, 13346834, 45152016, 152748176, 516743378, 1748130326, 5913882532, 20006521300, 67681576758, 228965134106, 774583500376, 2620397211992, 8864740270458

Offset

1,2

Comments

Column 2 of A231063.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + a(n-2) + a(n-3).

Empirical g.f.: 2*x^2 / (1 - 3*x - x^2 - x^3). - Colin Barker, Feb 24 2018

Example

Some solutions for n=4:
..0..1....0..3....0..3....0..1....0..1....0..1....0..1....0..1....0..3....0..1
..1..2....1..2....1..0....3..2....3..2....3..2....3..2....3..2....1..2....1..2
..2..3....0..3....2..3....1..0....2..1....0..3....2..1....2..3....0..1....0..3
..1..0....3..2....1..2....2..3....3..0....1..2....1..0....1..0....3..2....1..2

Crossrefs

Cf. A231063.

Sequence in context: A027063 A291005 A027065 * A295873 A006012 A127152

Adjacent sequences: A231054 A231055 A231056 * A231058 A231059 A231060

Keyword

nonn

Author

R. H. Hardin, Nov 03 2013

Status

approved