A230893 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, no adjacent elements equal, and upper left element zero.

0, 2, 2, 10, 22, 70, 186, 538, 1494, 4230, 11866, 33434, 94006, 264582, 744314, 2094362, 5892502, 16579462, 46647706, 131248794, 369281782, 1039014534, 2923376826, 8225233690, 23142568790, 65114084998, 183205408986, 515467935386

Offset

1,2

Comments

Column 2 of A230899.

Links

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

Formula

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

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

Example

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

Crossrefs

Cf. A230899.

Sequence in context: A192309 A151456 A336490 * A151389 A151428 A341680

Adjacent sequences: A230890 A230891 A230892 * A230894 A230895 A230896

Keyword

nonn

Author

R. H. Hardin, Oct 31 2013

Status

approved