A196701 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,1,0,4,2 for x=0,1,2,3,4.

2, 11, 38, 136, 488, 1744, 6208, 22202, 79292, 282984, 1010760, 3609442, 12887556, 46021868, 164340008, 586827146, 2095503116, 7482801488, 26720080488, 95414259450, 340712829860, 1216643200052, 4344485254120, 15513628195858

Offset

1,1

Comments

Every 0 is next to zero 3's, every 1 is next to one 1's, every 2 is next to two 0's, every 3 is next to three 4's, every 4 is next to four 2's.

Column 2 of A196707.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = a(n-1) +4*a(n-2) +16*a(n-3) +9*a(n-4) -a(n-5) +2*a(n-6) +2*a(n-7) for n>8.

Empirical g.f.: x*(2 + 9*x + 19*x^2 + 22*x^3 + 6*x^4 + 7*x^5 + x^6 - 2*x^7) / (1 - x - 4*x^2 - 16*x^3 - 9*x^4 + x^5 - 2*x^6 - 2*x^7). - Colin Barker, May 09 2018

Example

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

Crossrefs

Sequence in context: A320540 A059673 A294152 * A196850 A203534 A166989

Adjacent sequences: A196698 A196699 A196700 * A196702 A196703 A196704

Keyword

nonn

Author

R. H. Hardin, Oct 05 2011

Status

approved