A206857 Number of n X 2 0..2 arrays avoiding the pattern z z+1 z in any row, column, diagonal or antidiagonal.

9, 81, 625, 4761, 36481, 279841, 2146225, 16459249, 126225225, 968018769, 7423717921, 56932346025, 436613028289, 3348376640449, 25678633973281, 196928934060769, 1510244084935881, 11582031898782801, 88822372650180625

Offset

1,1

Comments

Column 2 of A206863.

Links

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

Formula

Empirical: a(n) = 8*a(n-1) -5*a(n-2) +18*a(n-3) +7*a(n-4) -2*a(n-5) -a(n-6).

Empirical g.f.: x*(9 + 9*x + 22*x^2 + 4*x^3 - 3*x^4 - x^5) / ((1 - x + 3*x^2 - x^3)*(1 - 7*x - 5*x^2 - x^3)). - Colin Barker, Feb 20 2018

Example

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

Crossrefs

Cf. A206863.

Sequence in context: A272243 A272242 A206728 * A073531 A206694 A125910

Adjacent sequences: A206854 A206855 A206856 * A206858 A206859 A206860

Keyword

nonn

Author

R. H. Hardin, Feb 13 2012

Status

approved