A243513 Number of length n+2 0..4 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..4 introduced in 0..4 order.

3, 5, 10, 24, 65, 187, 552, 1646, 4927, 14769, 44294, 132868, 398589, 1195751, 3587236, 10761690, 32285051, 96855133, 290565378, 871696112, 2615088313, 7845264915, 23535794720, 70607384134, 211822152375, 635466457097

Offset

1,1

Links

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

Formula

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

Conjectures from Colin Barker, Nov 02 2018: (Start)

G.f.: x*(3 - 10*x + 6*x^2) / ((1 - x)^2*(1 - 3*x)).

a(n) = (7 + 3^n + 2*n) / 4.

(End)

Example

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

Crossrefs

Column 4 of A243519.

Sequence in context: A209001 A240619 A171867 * A002039 A243514 A243515

Adjacent sequences: A243510 A243511 A243512 * A243514 A243515 A243516

Keyword

nonn

Author

R. H. Hardin, Jun 05 2014

Status

approved