A212823 Number of 0..2 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..2 order.

1, 2, 5, 12, 33, 90, 246, 672, 1836, 5016, 13704, 37440, 102288, 279456, 763488, 2085888, 5698752, 15569280, 42536064, 116210688, 317493504, 867408384, 2369803776, 6474424320, 17688456192, 48325761024, 132028434432, 360708390912

Offset

1,2

Comments

Column 2 of A212829.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) for n>5.

Empirical g.f.: x*(1 - x - x^2)*(1 + x + x^2) / (1 - 2*x - 2*x^2). - Colin Barker, Jul 21 2018

Example

Some solutions for n=8:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....0....1....1....1....0....1....1....1....1....1
..2....2....1....2....2....2....0....0....2....1....1....1....0....0....2....2
..1....0....0....2....2....0....1....2....0....1....2....2....2....0....0....0
..0....0....2....2....0....1....2....1....0....2....2....0....1....1....2....2
..0....1....0....0....1....1....2....0....0....0....0....0....0....2....2....2
..1....0....0....2....0....0....1....0....1....0....0....1....2....2....0....2
..1....0....1....2....0....2....2....0....1....0....2....0....1....0....1....0

Crossrefs

Cf. A212829.

Sequence in context: A209717 A000560 A292212 * A292213 A032124 A292214

Adjacent sequences: A212820 A212821 A212822 * A212824 A212825 A212826

Keyword

nonn

Author

R. H. Hardin, May 28 2012

Status

approved