A198474 Number of 2n X 2 0..2 arrays with values 0..2 introduced in row major order and each element equal to an odd number of horizontal and vertical neighbors.

2, 12, 76, 492, 3212, 21036, 137932, 904812, 5936396, 38950572, 255572812, 1676946156, 11003350412, 72199015212, 473737530316, 3108453529452, 20396281280012, 133831275048876, 878140974959692, 5761968373855212

Offset

1,1

Comments

Column 1 of A198477.

Links

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

Formula

Empirical: a(n) = 9*a(n-1) - 16*a(n-2).

Conjectures from Colin Barker, Mar 02 2018: (Start)

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

a(n) = (2^(-4-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..0....0..0....0..0....0..1....0..1....0..0....0..1....0..0....0..0
..0..1....1..1....1..1....1..1....0..1....0..1....1..2....0..1....1..1....1..1
..2..2....2..2....0..0....0..0....2..2....2..0....1..2....1..2....2..0....2..2
..1..1....1..1....1..1....2..2....0..0....2..0....0..0....1..2....2..0....0..0
..0..0....2..2....2..2....1..0....1..2....1..1....1..1....0..0....0..2....2..2
..1..1....1..1....0..0....1..0....1..2....2..2....2..2....1..1....0..2....1..1

Crossrefs

Cf. A198477.

Sequence in context: A052875 A037725 A037620 * A285489 A121680 A277478

Adjacent sequences: A198471 A198472 A198473 * A198475 A198476 A198477

Keyword

nonn

Author

R. H. Hardin, Oct 25 2011

Status

approved