A243514 Number of length n+2 0..5 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..5 introduced in 0..5 order.

3, 5, 10, 25, 76, 263, 978, 3773, 14824, 58771, 234046, 934121, 3732372, 14921279, 59668714, 238642069, 954502720, 3817879787, 15271256982, 61084503617, 244336965868, 977345766295, 3909378870850, 15637507094765, 62550011601816

Offset

1,1

Links

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

Formula

Empirical: a(n) = 8*a(n-1) - 21*a(n-2) + 22*a(n-3) - 8*a(n-4).

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

G.f.: x*(3 - 19*x + 33*x^2 - 16*x^3) / ((1 - x)^2*(1 - 2*x)*(1 - 4*x)).

a(n) = (26 + 9*2^n + 4^n + 6*n) / 18.

(End)

Example

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

Crossrefs

Column 5 of A243519.

Sequence in context: A171867 A243513 A002039 * A243515 A243516 A243517

Adjacent sequences: A243511 A243512 A243513 * A243515 A243516 A243517

Keyword

nonn

Author

R. H. Hardin, Jun 05 2014

Status

approved