A204624 Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.

96, 2049, 43734, 933462, 19923888, 425257068, 9076721064, 193734264456, 4135079723136, 88259474206608, 1883817316421472, 40208348322379872, 858210220662456576, 18317707978060726464, 390974632428061590144

Offset

1,1

Comments

Column 2 of A204630.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 22*a(n-1) -14*a(n-2).

Conjectures from Colin Barker, Jun 07 2018: (Start)

G.f.: 3*x*(32 - 21*x) / (1 - 22*x + 14*x^2).

a(n) = (3*(11+sqrt(107))^n*(31+3*sqrt(107)) + (11-sqrt(107))^n*(-93+9*sqrt(107))) / (4*sqrt(107)).

(End)

Example

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

Crossrefs

Cf. A204630.

Sequence in context: A159711 A268636 A233153 * A090449 A336677 A233709

Adjacent sequences: A204621 A204622 A204623 * A204625 A204626 A204627

Keyword

nonn

Author

R. H. Hardin, Jan 17 2012

Status

approved