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

Author

R. H. Hardin, Jun 08 2014

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Column 6 of A243641.

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