A210100 Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having one or three distinct values, and new values 0..2 introduced in row major order.

7, 30, 135, 614, 2799, 12766, 58231, 265622, 1211647, 5526990, 25211655, 115004294, 524598159, 2392982206, 10915714711, 49792609142, 227131616287, 1036072863150, 4726101083175, 21558359689574, 98339596281519, 448581262028446

Offset

1,1

Comments

Column 1 of A210107.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) - 7*a(n-2) + 2*a(n-3).

Conjectures from Colin Barker, Jul 14 2018: (Start)

G.f.: x*(7 - 12*x + 4*x^2) / ((1 - x)*(1 - 5*x + 2*x^2)).

a(n) = (1/2) + (2^(-2-n)*((5-sqrt(17))^n*(-11+3*sqrt(17)) + (5+sqrt(17))^n*(11+3*sqrt(17)))) / sqrt(17).

(End)

Example

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

Crossrefs

Cf. A210107.

Sequence in context: A369201 A220720 A024311 * A297080 A375308 A256981

Adjacent sequences: A210097 A210098 A210099 * A210101 A210102 A210103

Keyword

nonn

Author

R. H. Hardin, Mar 17 2012

Status

approved