A243635 Number of length n+2 0..4 arrays with no three unequal elements in a row and new values 0..4 introduced in 0..4 order.

4, 9, 21, 51, 127, 324, 844, 2242, 6062, 16655, 46411, 130937, 373349, 1074194, 3114146, 9085176, 26643492, 78470989, 231925649, 687430207, 2042284587, 6078844480, 18121207896, 54086361422, 161592030394, 483170313579

Offset

1,1

Links

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

Formula

Empirical: a(n) = 7*a(n-1) - 14*a(n-2) + 21*a(n-4) - 7*a(n-5) - 6*a(n-6).

Empirical g.f.: x*(4 - 19*x + 14*x^2 + 30*x^3 - 20*x^4 - 12*x^5) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 3*x)*(1 - 2*x - 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
..0....1....0....1....0....0....0....1....0....1....1....1....0....0....1....1
..1....1....1....1....1....0....1....1....1....1....0....0....1....1....0....1
..0....0....1....1....1....0....0....1....0....1....0....1....0....1....1....2
..1....1....1....1....2....1....0....2....0....0....2....0....0....2....0....1
..0....1....2....2....2....1....1....2....1....0....2....0....2....2....0....1
..0....1....1....2....1....1....1....0....1....0....0....0....2....0....0....0
..2....1....2....3....2....2....0....0....1....0....0....1....2....0....0....0

Crossrefs

Column 4 of A243641.

Sequence in context: A297296 A048582 A069231 * A243636 A243637 A243638

Adjacent sequences: A243632 A243633 A243634 * A243636 A243637 A243638

Keyword

nonn

Author

R. H. Hardin, Jun 08 2014

Status

approved