A206791 Number of n X 2 0..3 arrays avoiding the pattern z z+1 z in any row, column, diagonal or antidiagonal.

16, 256, 3721, 53824, 779689, 11296321, 163660849, 2371105636, 34352398336, 497694975625, 7210567562500, 104466163115161, 1513497951497401, 21927445030264225, 317683182247352464, 4602570164626581904

Offset

1,1

Comments

Column 2 of A206797.

Links

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

Formula

Empirical: a(n) = 15*a(n-1) -11*a(n-2) +51*a(n-3) +13*a(n-4) -3*a(n-5) -a(n-6).

a(n) = A206790(n)^2. - Mark van Hoeij, May 14 2013

Empirical g.f.: x*(16 + 16*x + 57*x^2 + 9*x^3 - 4*x^4 - x^5) / ((1 - x + 4*x^2 - x^3)*(1 - 14*x - 7*x^2 - x^3)). - Colin Barker, Feb 20 2018

Example

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

Crossrefs

Cf. A206790, A206797.

Sequence in context: A267929 A122609 A206571 * A221665 A227592 A206840

Adjacent sequences: A206788 A206789 A206790 * A206792 A206793 A206794

Keyword

nonn

Author

R. H. Hardin, Feb 12 2012

Status

approved