A231025 Number of n X 2 0..2 arrays x(i,j) with each element horizontally, vertically or antidiagonally next to at least one element with value (x(i,j)+1) mod 3 and at least one element with value (x(i,j)-1) mod 3, and upper left element zero.

0, 2, 12, 62, 344, 1864, 10162, 55324, 301278, 1640592, 8933808, 48648834, 264916012, 1442593630, 7855607976, 42777519416, 232943926258, 1268490401852, 6907533179198, 37614801461920, 204830473095648, 1115399286396802

Offset

1,2

Links

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

Formula

Empirical: a(n) = 4*a(n-1) + 8*a(n-2) - 4*a(n-4) + a(n-5).

Empirical g.f.: 2*x^2*(1 + 2*x - x^2) / (1 - 4*x - 8*x^2 + 4*x^4 - x^5). - Colin Barker, Sep 25 2018

Example

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

Crossrefs

Column 2 of A231031.

Sequence in context: A226506 A026076 A361812 * A330387 A368760 A272363

Adjacent sequences: A231022 A231023 A231024 * A231026 A231027 A231028

Keyword

nonn

Author

R. H. Hardin, Nov 03 2013

Status

approved