A243517 Number of length n+2 0..8 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..8 introduced in 0..8 order.

3, 5, 10, 25, 77, 280, 1157, 5296, 26406, 141585, 807064, 4837587, 30181075, 194210670, 1279159631, 8571132698, 58153599684, 398124806735, 2743173705258, 18987825983429, 131858977691833, 917797527716980, 6398758306106345

Offset

1,1

Links

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

Formula

Empirical: a(n) = 23*a(n-1) - 212*a(n-2) + 1010*a(n-3) - 2669*a(n-4) + 3887*a(n-5) - 2878*a(n-6) + 840*a(n-7).

Empirical g.f.: x*(3 - 64*x + 531*x^2 - 2175*x^3 + 4579*x^4 - 4607*x^5 + 1680*x^6) / ((1 - x)^2*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 7*x)). - Colin Barker, Nov 02 2018

Example

Some solutions for n=5:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....0....0....0....1....1....1....0....1....1....1
..2....2....2....2....2....2....1....0....0....2....2....2....0....2....2....2
..3....3....3....3....3....3....2....0....0....0....3....3....1....0....3....3
..4....1....0....0....0....0....3....0....0....3....4....1....2....3....1....4
..5....0....1....4....2....2....0....1....0....4....1....0....3....4....2....1
..0....4....3....5....1....4....4....2....0....2....3....2....4....0....3....5

Crossrefs

Column 8 of A243519.

Sequence in context: A243514 A243515 A243516 * A243518 A025486 A011969

Adjacent sequences: A243514 A243515 A243516 * A243518 A243519 A243520

Keyword

nonn

Author

R. H. Hardin, Jun 05 2014

Status

approved