A198508 Number of 2n X 2 0..4 arrays with values 0..4 introduced in row major order and each element unequal to exactly two horizontal and vertical neighbors.

4, 59, 1626, 52065, 1720080, 57202471, 1905005414, 63461666189, 2114248706396, 70438021997715, 2346711308830450, 78183030527210041, 2604746159812022824, 86779736758694997119, 2891154190334815424766, 96321709194421413316965

Offset

1,1

Comments

Column 1 of A198511.

Links

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

Formula

Empirical: a(n) = 51*a(n-1) -691*a(n-2) +3601*a(n-3) -7056*a(n-4) +4096*a(n-5).

Empirical g.f.: x*(4 - 145*x + 1381*x^2 - 4496*x^3 + 4096*x^4) / ((1 - x)*(1 - 9*x + 16*x^2)*(1 - 41*x + 256*x^2)). - Colin Barker, May 14 2018

Example

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

Crossrefs

Cf. A198511.

Sequence in context: A257069 A199107 A280668 * A126754 A264820 A194534

Adjacent sequences: A198505 A198506 A198507 * A198509 A198510 A198511

Keyword

nonn

Author

R. H. Hardin, Oct 25 2011

Status

approved