A197642 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,2,2,0,2 for x=0,1,2,3,4.

1, 2, 11, 31, 66, 185, 595, 1760, 4857, 13817, 40388, 117255, 336113, 965514, 2786619, 8042407, 23164130, 66711425, 192263523, 554192616, 1596983385, 4601566433, 13260282324, 38213747983, 110121270385, 317332109746, 914453225419

Offset

1,2

Comments

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

Column 2 of A197648.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) +a(n-2) +a(n-3) +14*a(n-4) -9*a(n-5) -8*a(n-6).

Empirical g.f.: x*(1 + 6*x^2 + 6*x^3 - 23*x^4 - 8*x^5) / ((1 - x)*(1 - x - 2*x^2 - 3*x^3 - 17*x^4 - 8*x^5)). - Colin Barker, May 14 2018

Example

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

Crossrefs

Cf. A197648.

Sequence in context: A158295 A213898 A085041 * A121346 A106847 A092761

Adjacent sequences: A197639 A197640 A197641 * A197643 A197644 A197645

Keyword

nonn

Author

R. H. Hardin, Oct 16 2011

Status

approved