A243727 Number of length n+2 0..8 arrays with no three unequal elements in a row and no three equal elements in a row and new values 0..8 introduced in 0..8 order.

3, 6, 12, 25, 53, 116, 259, 594, 1389, 3323, 8095, 20113, 50814, 130632, 341034, 904330, 2432401, 6636002, 18344597, 51376058, 145658087, 417937885, 1212891031, 3558923683, 10552653608, 31606799640, 95575235380, 291651970212

Offset

1,1

Links

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

Formula

Empirical: a(n) = 8*a(n-1) - 139*a(n-3) + 196*a(n-4) + 960*a(n-5) - 1827*a(n-6) - 3456*a(n-7) + 7076*a(n-8) + 7239*a(n-9) - 12860*a(n-10) - 9148*a(n-11) + 9072*a(n-12) + 5760*a(n-13).

Empirical g.f.: x*(3 - 18*x - 36*x^2 + 346*x^3 + 99*x^4 - 2696*x^5 + 175*x^6 + 10799*x^7 - 195*x^8 - 22430*x^9 - 4582*x^10 + 19296*x^11 + 9401*x^12) / ((1 - 2*x)*(1 + 2*x)*(1 - 3*x)*(1 - x - x^2)*(1 - x - 3*x^2)*(1 - x - 4*x^2)*(1 - x - 5*x^2)*(1 - x - 8*x^2)). - Colin Barker, Nov 03 2018

Example

Some solutions for n=6:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....1....0....1....1....1....1....1....0....1....0....1....1....0....0....1
..1....0....1....1....0....0....0....0....1....0....1....0....0....1....1....0
..0....0....1....2....1....0....0....0....0....1....1....0....1....0....1....0
..0....2....2....2....0....1....1....2....0....0....2....1....0....0....0....2
..2....0....1....3....1....0....1....2....1....0....1....0....1....2....1....2
..0....2....1....2....0....1....2....0....1....1....1....1....1....0....0....0
..0....2....3....3....0....0....2....2....0....1....2....1....0....2....0....0

Crossrefs

Column 8 of A243729.

Sequence in context: A243724 A243725 A243726 * A243728 A243721 A280109

Adjacent sequences: A243724 A243725 A243726 * A243728 A243729 A243730

Keyword

nonn

Author

R. H. Hardin, Jun 09 2014

Status

approved