A230800 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 and at least one element with value (x(i,j)-1) mod 4, and upper left element zero.

0, 2, 2, 16, 34, 154, 432, 1618, 5058, 17664, 57586, 195866, 648928, 2185122, 7284482, 24435056, 81651394, 273490714, 914714512, 3062116338, 10245066178, 34289257824, 114738331026, 383986878106, 1284957453248, 4300144520002

Offset

1,2

Comments

Column 2 of A230805.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 6*a(n-2) - 5*a(n-3).

Empirical g.f.: 2*x^2*(1 - x) / (1 - 2*x - 6*x^2 + 5*x^3). - Colin Barker, Mar 17 2018

Example

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

Crossrefs

Cf. A230805.

Sequence in context: A353912 A303567 A177832 * A363236 A076615 A098777

Adjacent sequences: A230797 A230798 A230799 * A230801 A230802 A230803

Keyword

nonn

Author

R. H. Hardin, Oct 30 2013

Status

approved