A198287 Number of 2n X 2 0..3 arrays with values 0..3 introduced in row major order and each element equal to exactly one horizontal and vertical neighbor.

2, 17, 272, 4667, 80702, 1397477, 24207692, 419373647, 7265397242, 125869473977, 2180631250952, 37778460128867, 654494991508022, 11338834542738317, 196440265628093252, 3403240245856247927, 58959623892961901042

Offset

1,1

Comments

Column 1 of A198290.

Links

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

Formula

Empirical: a(n) = 23*a(n-1) - 103*a(n-2) + 81*a(n-3).

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

G.f.: x*(2 - 29*x + 87*x^2) / ((1 - x)*(1 - 22*x + 81*x^2)).

a(n) = (216 - (11-2*sqrt(10))^n*(-8+sqrt(10)) + (8+sqrt(10))*(11+2*sqrt(10))^n) / 216.

(End)

Example

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

Crossrefs

Cf. A198290.

Sequence in context: A195443 A176585 A086534 * A338635 A268705 A078367

Adjacent sequences: A198284 A198285 A198286 * A198288 A198289 A198290

Keyword

nonn

Author

R. H. Hardin, Oct 23 2011

Status

approved