A232901 Number of (n+1) X (1+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally or antidiagonally.

0, 4, 8, 12, 32, 84, 184, 412, 976, 2276, 5224, 12076, 28032, 64884, 150040, 347324, 804144, 1861124, 4307400, 9970252, 23077600, 53414548, 123632504, 286160860, 662347408, 1533063972, 3548423976, 8213173612, 19010179136, 44000880564

Offset

1,2

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - a(n-2) + 4*a(n-3).

Empirical g.f.: 4*x^2 / (1 - 2*x + x^2 - 4*x^3). - Colin Barker, Oct 06 2018

Example

Some solutions for n=5:
..2..1....0..1....2..1....0..1....2..1....2..1....0..1....0..1....2..1....0..1
..0..2....2..0....0..2....2..2....0..0....0..0....2..1....2..1....0..2....2..1
..1..0....1..2....1..0....1..0....1..2....1..2....0..0....0..1....1..0....0..1
..2..1....0..1....0..1....0..1....0..1....2..1....1..2....2..1....1..2....2..0
..0..2....2..2....2..0....2..2....2..2....0..2....1..0....0..0....1..0....1..2
..1..0....1..0....1..2....1..0....1..0....1..0....1..2....1..2....1..2....1..0

Crossrefs

Column 1 of A232908.

Sequence in context: A370134 A035403 A050908 * A038563 A083492 A137337

Adjacent sequences: A232898 A232899 A232900 * A232902 A232903 A232904

Keyword

nonn

Author

R. H. Hardin, Dec 02 2013

Status

approved