A210167 Number of (n+1) X 2 0..3 arrays containing all values 0..3 with every 2 X 2 subblock having two or four distinct values, and new values 0..3 introduced in row major order.

1, 10, 101, 910, 7545, 59178, 447429, 3300982, 23953969, 171879010, 1223834045, 8668104046, 61170701289, 430597896090, 3025851581877, 21237517730278, 148936511331361, 1043880899831122, 7313575755465773, 51226014364080862

Offset

1,2

Comments

Column 1 of A210174.

Links

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

Formula

Empirical: a(n) = 14*a(n-1) - 55*a(n-2) + 22*a(n-3) + 132*a(n-4) + 56*a(n-5).

Empirical g.f.: x*(1 - 4*x + 16*x^2 + 24*x^3 + 8*x^4) / ((1 - 7*x)*(1 - 3*x - 2*x^2)*(1 - 4*x - 4*x^2)). - Colin Barker, Jul 15 2018

Example

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

Crossrefs

Cf. A210174.

Sequence in context: A219763 A214390 A293804 * A288790 A280371 A105032

Adjacent sequences: A210164 A210165 A210166 * A210168 A210169 A210170

Keyword

nonn

Author

R. H. Hardin, Mar 18 2012

Status

approved