A230904 Number of n X 2 0..3 arrays x(i,j) with each element horizontally, vertically or antidiagonally 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, 8, 26, 84, 272, 882, 2862, 9290, 30160, 97922, 317940, 1032328, 3351922, 10883582, 35338706, 114743960, 372571146, 1209730676, 3927970464, 12754039410, 41412104942, 134464258714, 436602703328, 1417640069298, 4603048385236

Offset

1,2

Links

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

Formula

Empirical: a(n) = 5*a(n-1) -6*a(n-2) +a(n-3) for n>4.

Empirical g.f.: 2*x^2*(1 - x - x^2) / (1 - 5*x + 6*x^2 - x^3). - Colin Barker, Sep 22 2018

Example

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

Crossrefs

Column 2 of A230910.

Sequence in context: A002930 A060410 A128634 * A289595 A343485 A298189

Adjacent sequences: A230901 A230902 A230903 * A230905 A230906 A230907

Keyword

nonn

Author

R. H. Hardin, Nov 01 2013

Status

approved