A197883 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,1,1 for x=0,1,2,3,4.

0, 4, 3, 14, 18, 43, 78, 154, 305, 572, 1178, 2185, 4440, 8408, 16795, 32212, 63608, 123295, 241494, 470486, 918795, 1793434, 3497978, 6831997, 13324168, 26019470, 50755921, 99095168, 193344576, 377408195, 736481712, 1437442548, 2805273219

Offset

1,2

Comments

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

Column 2 of A197889.

Links

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

Formula

Empirical: a(n) = 3*a(n-2) +2*a(n-3) +a(n-4) -3*a(n-5) -4*a(n-6) +7*a(n-7) -5*a(n-9).

Empirical g.f.: x^2*(4 + 3*x + 2*x^2 + x^3 - 9*x^4 + 5*x^5 - 7*x^7) / ((1 - x)*(1 + x - 2*x^2 - 4*x^3 - 5*x^4 - 2*x^5 + 2*x^6 - 5*x^7 - 5*x^8)). - Colin Barker, May 14 2018

Example

Some solutions for n=4:
..2..1....2..1....1..2....1..2....2..1....1..2....0..1....2..1....0..1....1..2
..1..3....1..3....3..1....3..1....1..0....0..1....1..2....1..0....1..2....0..1
..3..1....0..1....1..3....1..0....1..2....2..1....1..2....3..1....1..0....1..0
..1..2....1..2....2..1....2..1....0..1....1..0....0..1....1..2....2..1....2..1

Crossrefs

Cf. A197889.

Sequence in context: A056480 A284841 A334752 * A222195 A292413 A305255

Adjacent sequences: A197880 A197881 A197882 * A197884 A197885 A197886

Keyword

nonn

Author

R. H. Hardin, Oct 19 2011

Status

approved