A198638 Number of 2n X 2 0..2 arrays with values 0..2 introduced in row major order and each element equal to an even number of horizontal and vertical neighbors.

4, 36, 376, 3936, 41216, 431616, 4519936, 47333376, 495681536, 5190844416, 54359228416, 569257230336, 5961339109376, 62427953627136, 653754017775616, 6846200955273216, 71694347178868736, 750792950862053376

Offset

1,1

Comments

Column 1 of A198642.

Links

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

Formula

Empirical: a(n) = 12*a(n-1) -16*a(n-2) for n>3.

Conjectures from Colin Barker, May 15 2018: (Start)

G.f.: 4*x*(1 - x)*(1 - 2*x) / (1 - 12*x + 16*x^2).

a(n) = ((6 - 2*sqrt(5))^n*(-5+3*sqrt(5)) + (2*(3+sqrt(5)))^n*(5+3*sqrt(5))) / (16*sqrt(5)) for n>1.

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

Crossrefs

Cf. A198642.

Sequence in context: A138736 A372461 A266093 * A358954 A019999 A291274

Adjacent sequences: A198635 A198636 A198637 * A198639 A198640 A198641

Keyword

nonn

Author

R. H. Hardin, Oct 27 2011

Status

approved