A198447 Number of 2n X 2 0..2 arrays with values 0..2 introduced in row major order and each element unequal to exactly two horizontal and vertical neighbors.

3, 13, 71, 433, 2763, 17941, 117263, 768313, 5038611, 33054493, 216872663, 1422982081, 9336876123, 61264171813, 401987528351, 2637661006153, 17307148601763, 113561761317421, 745141474228583, 4889285086978513

Offset

1,1

Comments

Column 1 of A198452.

Links

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

Formula

Empirical: a(n) = 10*a(n-1) -25*a(n-2) +16*a(n-3).

Conjectures from Colin Barker, May 14 2018: (Start)

G.f.: x*(3 - 17*x + 16*x^2) / ((1 - x)*(1 - 9*x + 16*x^2)).

a(n) = 1/4 + (2^(-3-n)*((9+sqrt(17))^n*(-5+3*sqrt(17)) + (9-sqrt(17))^n*(5+3*sqrt(17)))) / sqrt(17).

(End)

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
..1..0....1..2....2..0....1..2....2..2....2..0....2..2....2..0....2..2....2..0
..1..0....1..2....2..0....1..2....1..1....2..0....1..1....2..0....1..1....2..0
..2..2....2..0....0..2....2..1....0..2....1..1....2..2....0..1....2..2....1..2
..1..1....2..0....0..2....2..1....0..2....2..2....1..1....0..1....0..0....1..2
..2..0....0..2....2..1....0..2....1..0....1..0....2..0....2..0....1..2....0..1

Crossrefs

Cf. A198452.

Sequence in context: A227117 A277922 A182189 * A318223 A162326 A122455

Adjacent sequences: A198444 A198445 A198446 * A198448 A198449 A198450

Keyword

nonn

Author

R. H. Hardin, Oct 25 2011

Status

approved