A198717 Number of n X 2 0..6 arrays with values 0..6 introduced in row major order and no element equal to any horizontal or vertical neighbor.

1, 4, 34, 499, 10507, 272410, 7817980, 234638905, 7176366133, 221220625936, 6841771033846, 211886983790431, 6565800345745279, 203504808219690982, 6308194354577750032, 195548116214389189477, 6061914804816147034345

Offset

1,2

Comments

Column 2 of A198723.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 55*a(n-1) - 918*a(n-2) + 5818*a(n-3) - 13417*a(n-4) + 8463*a(n-5).

Conjectures from Colin Barker, Feb 22 2018: (Start)

G.f.: x*(1 - 51*x + 732*x^2 - 3517*x^3 + 4419*x^4) / ((1 - x)*(1 - 3*x)*(1 - 7*x)*(1 - 13*x)*(1 - 31*x)).

a(n) = 11/30 + 3^n/8 + 7^(n-1)/6 + 13^(n-1)/12 + 31^(n-1)/120.

(End)

Example

Some solutions with all values 0 to 6 for n=4:
..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
..2..3....2..3....2..3....2..3....2..3....2..3....2..0....2..3....2..3....2..3
..4..5....4..5....4..5....4..5....4..1....4..5....3..4....4..5....4..0....1..4
..6..1....6..0....2..6....6..2....5..6....6..4....5..6....0..6....5..6....5..6

Crossrefs

Cf. A198723.

Sequence in context: A111169 A274244 A002105 * A198908 A207864 A222077

Adjacent sequences: A198714 A198715 A198716 * A198718 A198719 A198720

Keyword

nonn

Author

R. H. Hardin, Oct 29 2011

Status

approved