A243518 Number of length n+2 0..9 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..9 introduced in 0..9 order.

3, 5, 10, 25, 77, 280, 1157, 5297, 26443, 142372, 819731, 5009281, 32252381, 217194296, 1518771097, 10952508217, 80950970231, 609958242292, 4664758144295, 36080343085145, 281462510140633, 2209800140157400, 17432715938447165

Offset

1,1

Links

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

Formula

Empirical: a(n) = 30*a(n-1) - 372*a(n-2) + 2478*a(n-3) - 9639*a(n-4) + 22260*a(n-5) - 29588*a(n-6) + 20592*a(n-7) - 5760*a(n-8).

Empirical g.f.: x*(3 - 85*x + 976*x^2 - 5849*x^3 + 19574*x^4 - 36095*x^5 + 33305*x^6 - 11520*x^7) / ((1 - x)^2*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 8*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....0....1....0....1....0....1....0....1....1....0....1....1....1....1
..2....2....1....2....0....2....0....2....1....2....2....1....2....2....2....2
..3....3....2....3....0....3....1....3....2....0....0....2....3....3....0....3
..4....0....3....4....1....0....2....1....3....3....3....0....1....0....3....1
..1....4....0....0....2....1....3....4....1....4....1....1....4....1....4....4
..2....2....1....2....3....3....1....3....4....1....4....2....0....2....5....5

Crossrefs

Column 9 of A243519.

Sequence in context: A243515 A243516 A243517 * A025486 A011969 A003187

Adjacent sequences: A243515 A243516 A243517 * A243519 A243520 A243521

Keyword

nonn

Author

R. H. Hardin, Jun 05 2014

Status

approved