A210302 Number of (n+1) X 2 0..3 arrays containing all values 0..3 with every 2 X 2 subblock having one or three distinct values, and new values 0..3 introduced in row major order.

0, 29, 414, 4553, 45890, 446093, 4266246, 40490097, 382887722, 3614390197, 34090440494, 321405533785, 3029622853138, 28555016231773, 269126357016278, 2536415298825665, 23904507782220922, 225287438517410949

Offset

1,2

Comments

Column 1 of A210309.

Links

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

Formula

Empirical: a(n) = 15*a(n-1) - 57*a(n-2) + 41*a(n-3) + 10*a(n-4) - 8*a(n-5).

Empirical g.f.: x^2*(29 - 21*x - 4*x^2 + 4*x^3) / ((1 - x)*(1 - 5*x + 2*x^2)*(1 - 9*x - 4*x^2)). - Colin Barker, Jul 15 2018

Example

Some solutions for n=4:
..0..1....0..0....0..0....0..0....0..1....0..1....0..0....0..0....0..0....0..0
..1..2....1..2....0..0....0..0....1..2....1..2....0..0....0..0....1..2....0..0
..3..3....2..3....0..0....0..0....2..3....2..3....0..0....1..2....3..1....1..2
..3..3....2..1....1..2....1..2....1..1....2..0....1..2....3..2....1..0....1..3
..3..3....1..0....3..1....3..2....0..3....0..1....1..3....3..0....0..2....0..0

Crossrefs

Cf. A210309.

Sequence in context: A042630 A174885 A264160 * A163021 A125464 A161572

Adjacent sequences: A210299 A210300 A210301 * A210303 A210304 A210305

Keyword

nonn

Author

R. H. Hardin, Mar 19 2012

Status

approved