A243039 Number of length n+3 0..3 arrays with no four elements in a row with pattern abab (with a!=b) and new values 0..3 introduced in 0..3 order.

14, 46, 163, 602, 2271, 8655, 33148, 127255, 489084, 1880732, 7234069, 27828644, 107059965, 411883517, 1584628966, 6096542009, 23455294538, 90239951178, 347181934423, 1335720317278, 5138945540059, 19771177361419, 76066085076416

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 3*a(n-2) - 5*a(n-3) - 3*a(n-4) + 3*a(n-5) + 3*a(n-6) + a(n-7).

Empirical g.f.: x*(14 - 24*x - 25*x^2 - 5*x^3 + 22*x^4 + 17*x^5 + 5*x^6) / ((1 - x)*(1 - x - x^2 - x^3)*(1 - 3*x - 3*x^2 - x^3)). - Colin Barker, Nov 01 2018

Example

Some solutions for n=4:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....0....1....1....1....0....1....1....1....1....1....1....0....0....1
..2....2....1....1....2....2....0....0....2....2....2....2....1....0....1....0
..3....1....2....2....1....0....1....2....1....2....0....2....0....0....0....0
..0....3....3....3....0....0....1....2....1....2....2....2....2....1....2....2
..3....1....1....3....3....3....2....2....1....3....1....0....0....2....3....1
..2....2....0....0....0....3....2....1....2....2....0....2....1....1....0....2

Crossrefs

Column 3 of A243044.

Sequence in context: A233367 A211919 A233361 * A243385 A242580 A243386

Adjacent sequences: A243036 A243037 A243038 * A243040 A243041 A243042

Keyword

nonn

Author

R. H. Hardin, May 29 2014

Status

approved