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

Author

R. H. Hardin, May 28 2012

Keywords

• nonn

Comments

Column 3 of A212829.

Examples

			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
		

Links

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

Crossrefs

Cf. A212829.

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