A234779 Number of (n+1) X (1+1) 0..3 arrays with no adjacent elements equal and with each 2 X 2 subblock having the number of clockwise edge increases equal to the number of counterclockwise edge increases.

76, 484, 3084, 19652, 125228, 797988, 5085004, 32403076, 206481516, 1315758308, 8384382092, 53427641412, 340455961516, 2169481164964, 13824544308684, 88093885500932, 561359021271788, 3577137606898788, 22794527163204364

Offset

1,1

Links

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

Formula

Empirical: a(n) = 7*a(n-1) - 4*a(n-2).

Conjectures from Colin Barker, Oct 16 2018: (Start)

G.f.: 4*x*(19 - 12*x) / (1 - 7*x + 4*x^2).

a(n) = (2^(1-n)*((7-sqrt(33))^n*(-17+3*sqrt(33)) + (7+sqrt(33))^n*(17+3*sqrt(33)))) / sqrt(33).

(End)

Example

Some solutions for n=5:
..3..2....2..0....1..0....2..3....3..2....3..2....1..0....1..2....2..0....2..1
..2..1....0..3....0..1....1..2....2..1....2..1....2..1....2..0....1..3....0..2
..0..2....2..1....2..3....3..0....1..3....0..3....0..3....1..3....3..1....1..3
..2..0....1..3....0..1....2..3....2..0....3..0....3..2....2..0....1..3....0..1
..0..3....0..1....2..3....0..1....0..1....0..2....0..3....3..2....0..1....1..3
..3..0....3..0....3..2....1..0....3..0....1..3....3..0....2..1....1..3....2..1

Crossrefs

Column 1 of A234786.

Sequence in context: A205919 A238918 A234786 * A264475 A363843 A262790

Adjacent sequences: A234776 A234777 A234778 * A234780 A234781 A234782

Keyword

nonn

Author

R. H. Hardin, Dec 30 2013

Status

approved