A243516 Number of length n+2 0..7 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..7 introduced in 0..7 order.

3, 5, 10, 25, 77, 280, 1156, 5267, 25915, 135214, 736706, 4139833, 23767897, 138468212, 814675840, 4824766303, 28699128503, 171207852154, 1023332115838, 6124430348357, 36684624841813, 219860794899520, 1318179574171580

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
..0....0....0....1....0....1....1....1....0....1
..1....0....0....2....1....2....2....2....0....2
..2....0....1....3....2....3....0....3....0....0
..3....1....2....0....0....4....3....1....0....1
		

Links

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

Crossrefs

Column 7 of A243519.

Formula

Empirical: a(n) = 17*a(n-1) - 111*a(n-2) + 355*a(n-3) - 584*a(n-4) + 468*a(n-5) - 144*a(n-6).

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

G.f.: x*(3 - 46*x + 258*x^2 - 655*x^3 + 739*x^4 - 288*x^5) / ((1 - x)^2*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 6*x)).

a(n) = (2722 + 675*2^n + 25*2^(1+2*n) + 50*3^(1+n) + 2^n*3^(1+n) + 660*n) / 1800.

(End)