A197201 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,2,1,0,3 for x=0,1,2,3,4.

1, 5, 16, 47, 154, 496, 1601, 5183, 16777, 54298, 175777, 569008, 1841952, 5962675, 19302067, 62483633, 202268864, 654774451, 2119602518, 6861469468, 22211599969, 71902261547, 232758343993, 753473472226, 2439106000077, 7895749882524

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

Column 2 of A197207.

Links

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

Formula

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

Empirical g.f.: x*(1 + x)*(1 + 2*x - 7*x^3 - 3*x^4 - x^5 + 4*x^6) / (1 - 2*x - 4*x^2 - 2*x^3 + 4*x^4 + 8*x^5 - x^7 - 2*x^8). - Colin Barker, Mar 01 2018

Example

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

Crossrefs

Cf. A197207.

Sequence in context: A094586 A353133 A140336 * A166868 A055144 A171426

Adjacent sequences: A197198 A197199 A197200 * A197202 A197203 A197204

Keyword

nonn

Author

R. H. Hardin, Oct 11 2011

Status

approved