A243515 - OEIS

A243515

Number of length n+2 0..6 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..6 introduced in 0..6 order.

3, 5, 10, 25, 77, 279, 1134, 4979, 22981, 109453, 531458, 2610933, 12917685, 64181627, 319695982, 1594859887, 7963472189, 39784944801, 198827606706, 993846943841, 4968361974493, 24839192686975, 124188113975630

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OFFSET

1,1

LINKS

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

FORMULA

Empirical: a(n) = 12*a(n-1) - 52*a(n-2) + 102*a(n-3) - 91*a(n-4) + 30*a(n-5).

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

G.f.: x*(3 - 31*x + 106*x^2 - 141*x^3 + 60*x^4) / ((1 - x)^2*(1 - 2*x)*(1 - 3*x)*(1 - 5*x)).

a(n) = (147 + 2^(5+n) + 4*3^(1+n) + 5^n + 36*n) / 96.

(End)

EXAMPLE

All solutions for n=3:

..0....0....0....0....0....0....0....0....0....0

..1....0....1....0....1....1....0....1....0....0

..2....1....2....0....2....2....0....2....1....0

..3....2....3....1....0....3....0....0....2....0

..1....0....0....2....3....4....1....1....3....0

CROSSREFS

Column 6 of A243519.

Sequence in context: A243513 A002039 A243514 * A243516 A243517 A243518

Adjacent sequences: A243512 A243513 A243514 * A243516 A243517 A243518

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jun 05 2014

STATUS

approved