A243637 Number of length n+2 0..6 arrays with no three unequal elements in a row and new values 0..6 introduced in 0..6 order.

4, 9, 21, 51, 127, 324, 844, 2243, 6073, 16737, 46905, 133555, 386047, 1131958, 3364454, 10129563, 30871733, 95176427, 296618011, 933821451, 2967726939, 9514201392, 30747183016, 100097739315, 328049191105, 1081610514581

Offset

1,1

Links

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

Formula

Empirical: a(n) = 11*a(n-1) - 39*a(n-2) + 21*a(n-3) + 151*a(n-4) - 217*a(n-5) - 181*a(n-6) + 339*a(n-7) + 130*a(n-8) - 154*a(n-9) - 60*a(n-10).

Empirical g.f.: x*(4 - 35*x + 78*x^2 + 87*x^3 - 408*x^4 - 16*x^5 + 668*x^6 + 57*x^7 - 368*x^8 - 120*x^9) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 3*x)*(1 - 2*x - x^2)*(1 - 2*x - 2*x^2)*(1 - 2*x - 5*x^2)). - Colin Barker, Nov 02 2018

Example

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

Crossrefs

Column 6 of A243641.

Sequence in context: A069231 A243635 A243636 * A243638 A243639 A243640

Adjacent sequences: A243634 A243635 A243636 * A243638 A243639 A243640

Keyword

nonn

Author

R. H. Hardin, Jun 08 2014

Status

approved