A243513 Number of length n+2 0..4 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..4 introduced in 0..4 order.

3, 5, 10, 24, 65, 187, 552, 1646, 4927, 14769, 44294, 132868, 398589, 1195751, 3587236, 10761690, 32285051, 96855133, 290565378, 871696112, 2615088313, 7845264915, 23535794720, 70607384134, 211822152375, 635466457097

Offset: 1

Author

R. H. Hardin, Jun 05 2014

Keywords

• nonn

Examples

			All solutions for n=3:
..0....0....0....0....0....0....0....0....0....0
..1....0....1....0....0....1....1....1....0....0
..2....0....2....1....0....2....2....2....0....1
..3....1....0....2....0....0....3....3....0....2
..0....2....1....3....1....3....1....4....0....0
		

Links

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

Crossrefs

Column 4 of A243519.

Formula

Empirical: a(n) = 5*a(n-1) - 7*a(n-2) + 3*a(n-3).

Conjectures from Colin Barker, Nov 02 2018: (Start)

G.f.: x*(3 - 10*x + 6*x^2) / ((1 - x)^2*(1 - 3*x)).

a(n) = (7 + 3^n + 2*n) / 4.

(End)