A243600 Number of length n+2 0..3 arrays with no three elements in a row with pattern aba (with a!=b) and new values 0..3 introduced in 0..3 order.

4, 10, 28, 85, 269, 870, 2844, 9346, 30792, 101577, 335289, 1107066, 3655876, 12073706, 39875396, 131697309, 434963141, 1436579966, 4744692092, 15670638530, 51756579024, 170940329233, 564577491697, 1864672682930, 6158595344068

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 5*a(n-2) - 3*a(n-3) + 3*a(n-4) + a(n-5).

Empirical g.f.: x*(4 - 10*x - 2*x^2 + 7*x^3 + 2*x^4) / ((1 - x)*(1 - x - x^2)*(1 - 3*x - x^2)). - 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....0....1....0....0....1....1....1....0....0....0....1....1....1....1....1
..2....1....2....0....1....2....2....2....1....1....0....2....2....1....1....2
..3....2....2....1....2....0....3....3....2....1....0....3....3....2....2....2
..3....2....1....1....2....3....1....3....0....2....1....0....3....3....2....0
..1....3....0....1....2....3....0....3....3....3....1....0....3....0....0....0
..2....0....3....0....0....2....2....1....1....1....2....1....3....1....1....2

Crossrefs

Column 3 of A243607.

Sequence in context: A083587 A228403 A061639 * A239577 A008995 A111236

Adjacent sequences: A243597 A243598 A243599 * A243601 A243602 A243603

Keyword

nonn

Author

R. H. Hardin, Jun 07 2014

Status

approved