A232584 Number of (n+1)X(3+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally or antidiagonally, with no adjacent elements equal

2, 12, 42, 122, 332, 882, 2322, 6092, 15962, 41802, 109452, 286562, 750242, 1964172, 5142282, 13462682, 35245772, 92274642, 241578162, 632459852, 1655801402, 4334944362, 11349031692, 29712150722, 77787420482, 203650110732

Offset

1,1

Comments

Column 3 of A232589.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) -4*a(n-2) +a(n-3) = 2*A122678(n).

Empirical: G.f.: -2*x*(1+x)^2 / ( (x-1)*(x^2-3*x+1) ). - R. J. Mathar, Nov 23 2014

Example

Some solutions for n=7
..0..1..2..1....2..1..0..1....0..1..0..1....2..1..0..1....2..1..2..1
..2..1..0..1....0..1..2..1....2..1..2..1....2..1..2..0....0..1..0..1
..2..1..2..1....2..1..0..1....2..1..0..2....2..0..1..0....0..1..2..1
..0..1..0..1....2..1..2..0....0..2..1..2....1..2..1..0....0..1..0..2
..0..1..2..1....2..0..1..0....1..0..1..0....1..0..2..1....0..2..1..2
..0..1..0..2....1..2..1..2....1..2..1..2....2..1..0..2....1..0..1..2
..0..2..1..2....1..0..1..2....1..0..1..0....0..2..1..0....1..2..1..0
..1..0..1..2....1..2..1..0....1..2..1..2....1..0..1..2....1..0..1..2

Crossrefs

Sequence in context: A001621 A277935 A290928 * A189491 A301556 A055681

Adjacent sequences: A232581 A232582 A232583 * A232585 A232586 A232587

Keyword

nonn

Author

R. H. Hardin, Nov 26 2013

Status

approved