A196741 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,3,1,0,4 for x=0,1,2,3,4.

1, 3, 20, 71, 282, 1144, 4559, 18153, 72678, 290202, 1158957, 4630454, 18496588, 73884837, 295148260, 1179007713, 4709690448, 18813523020, 75153147188, 300209266280, 1199226506236, 4790471735629, 19136183610441, 76442062534904

Offset

1,2

Comments

Every 0 is next to 0 2's, every 1 is next to 1 3's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 4's.

Column 3 of A196746.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +5*a(n-2) +12*a(n-3) +2*a(n-4) -11*a(n-5) +4*a(n-6) -5*a(n-7) +a(n-8).

Empirical g.f.: x*(1 + x + 9*x^2 + 4*x^3 + 2*x^4 - 10*x^5 - 2*x^6 + 2*x^7) / (1 - 2*x - 5*x^2 - 12*x^3 - 2*x^4 + 11*x^5 - 4*x^6 + 5*x^7 - x^8). - Colin Barker, May 09 2018

Example

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

Crossrefs

Cf. A196746.

Sequence in context: A348208 A160456 A289643 * A196899 A006411 A243208

Adjacent sequences: A196738 A196739 A196740 * A196742 A196743 A196744

Keyword

nonn

Author

R. H. Hardin, Oct 06 2011

Status

approved