A243600 Number of length n+2 0..3 arrays with no three elements in a row with pattern aba (with a!=b) and new values 0..3 introduced in 0..3 order.

4, 10, 28, 85, 269, 870, 2844, 9346, 30792, 101577, 335289, 1107066, 3655876, 12073706, 39875396, 131697309, 434963141, 1436579966, 4744692092, 15670638530, 51756579024, 170940329233, 564577491697, 1864672682930, 6158595344068

Offset: 1

Author

R. H. Hardin, Jun 07 2014

Keywords

• nonn

Examples

			Some solutions for n=5:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....0....1....0....0....1....1....1....0....0....0....1....1....1....1....1
..2....1....2....0....1....2....2....2....1....1....0....2....2....1....1....2
..3....2....2....1....2....0....3....3....2....1....0....3....3....2....2....2
..3....2....1....1....2....3....1....3....0....2....1....0....3....3....2....0
..1....3....0....1....2....3....0....3....3....3....1....0....3....0....0....0
..2....0....3....0....0....2....2....1....1....1....2....1....3....1....1....2
		

Links

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

Crossrefs

Column 3 of A243607.

Formula

Empirical: a(n) = 5*a(n-1) - 5*a(n-2) - 3*a(n-3) + 3*a(n-4) + a(n-5).

Empirical g.f.: x*(4 - 10*x - 2*x^2 + 7*x^3 + 2*x^4) / ((1 - x)*(1 - x - x^2)*(1 - 3*x - x^2)). - Colin Barker, Nov 02 2018