A243516 Number of length n+2 0..7 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..7 introduced in 0..7 order.

3, 5, 10, 25, 77, 280, 1156, 5267, 25915, 135214, 736706, 4139833, 23767897, 138468212, 814675840, 4824766303, 28699128503, 171207852154, 1023332115838, 6124430348357, 36684624841813, 219860794899520, 1318179574171580

Offset

1,1

Links

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

Formula

Empirical: a(n) = 17*a(n-1) - 111*a(n-2) + 355*a(n-3) - 584*a(n-4) + 468*a(n-5) - 144*a(n-6).

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

G.f.: x*(3 - 46*x + 258*x^2 - 655*x^3 + 739*x^4 - 288*x^5) / ((1 - x)^2*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 6*x)).

a(n) = (2722 + 675*2^n + 25*2^(1+2*n) + 50*3^(1+n) + 2^n*3^(1+n) + 660*n) / 1800.

(End)

Example

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

Crossrefs

Column 7 of A243519.

Sequence in context: A002039 A243514 A243515 * A243517 A243518 A025486

Adjacent sequences: A243513 A243514 A243515 * A243517 A243518 A243519

Keyword

nonn

Author

R. H. Hardin, Jun 05 2014

Status

approved