A212824 Number of 0..3 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..3 order.

1, 2, 5, 13, 43, 152, 559, 2091, 7882, 29809, 112895, 427824, 1621691, 6147791, 23307226, 88363077, 335007715, 1270107208, 4815336407, 18256317315, 69214939274, 262413734345, 994885963543, 3771899000928, 14300354743363

Offset

1,2

Comments

Column 3 of A212829.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) + a(n-2) - 6*a(n-3) - 3*a(n-4) for n>7.

Empirical g.f.: x*(1 + x + x^2)*(1 - 3*x - 2*x^2 + 2*x^3 + x^4) / ((1 - x - x^2)*(1 - 3*x - 3*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
..0....1....1....1....1....1....1....1....1....0....1....1....1....0....1....1
..1....2....0....1....0....1....2....2....1....1....1....2....2....1....1....2
..2....3....2....2....2....2....0....0....2....2....0....3....2....2....0....2
..2....0....0....2....2....2....3....2....2....3....2....2....2....3....1....3
..0....2....3....3....3....0....2....1....0....1....3....1....0....3....1....1
..1....2....2....3....1....0....2....0....2....2....3....3....3....2....1....0
..1....0....1....2....0....0....1....3....3....0....2....1....0....0....2....0

Crossrefs

Cf. A212829.

Sequence in context: A299430 A307263 A278171 * A338660 A286949 A287023

Adjacent sequences: A212821 A212822 A212823 * A212825 A212826 A212827

Keyword

nonn

Author

R. H. Hardin, May 28 2012

Status

approved