A268093 Number of 1 X n 0..2 arrays with every repeated value in every row not one larger and in every column one larger mod 3 than the previous repeated value, and upper left element zero.

1, 3, 9, 26, 74, 208, 580, 1608, 4440, 12224, 33584, 92128, 252448, 691200, 1891392, 5173376, 14145920, 38671360, 105700096, 288873984, 789410304, 2157092864, 5894054912, 16104392704, 44001089536, 120219353088, 328457662464

Offset

1,2

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 2*a(n-2) - 4*a(n-3).

Conjectures from Colin Barker, Jan 11 2019: (Start)

G.f.: x*(1 - x - x^2) / ((1 - 2*x)*(1 - 2*x - 2*x^2)).

a(n) = (-3*2^n + (3-2*sqrt(3))*(1-sqrt(3))^n + (1+sqrt(3))^n*(3+2*sqrt(3))) / 12.

(End)

Example

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

Crossrefs

Row 1 of A268092.

Sequence in context: A061667 A234270 A258911 * A127911 A116423 A077845

Adjacent sequences: A268090 A268091 A268092 * A268094 A268095 A268096

Keyword

nonn

Author

R. H. Hardin, Jan 26 2016

Status

approved