A210406 Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having three or four distinct values, and new values 0..3 introduced in row major order.

7, 78, 864, 9576, 106128, 1176192, 13035456, 144468864, 1601114112, 17744767488, 196661044224, 2179547652096, 24155409051648, 267708662341632, 2966951532036096, 32882019268460544, 364423611069038592

Offset

1,1

Comments

Column 1 of A210413.

Links

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

Formula

Empirical: a(n) = 10*a(n-1) + 12*a(n-2).

Conjectures from Colin Barker, Jul 15 2018: (Start)

G.f.: x*(7 + 8*x) / (1 - 10*x - 12*x^2).

a(n) = ((5-sqrt(37))^n*(-11+2*sqrt(37)) + (5+sqrt(37))^n*(11+2*sqrt(37))) / (6*sqrt(37)).

(End)

Example

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

Crossrefs

Cf. A210413.

Sequence in context: A210413 A045485 A068621 * A133272 A186657 A079590

Adjacent sequences: A210403 A210404 A210405 * A210407 A210408 A210409

Keyword

nonn

Author

R. H. Hardin, Mar 21 2012

Status

approved