A238923 Number of (n+1) X (1+1) 0..3 arrays with no element greater than all horizontal neighbors or equal to all vertical neighbors.

12, 36, 144, 540, 2052, 7776, 29484, 111780, 423792, 1606716, 6091524, 23094720, 87558732, 331960356, 1258557264, 4771552860, 18090330372, 68585649696, 260027940204, 985840769700, 3737606129712, 14170340698236, 53723840483844

Offset

1,1

Links

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

Formula

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

Conjectures from Colin Barker, Oct 24 2018: (Start)

G.f.: 12*x / (1 - 3*x - 3*x^2).

a(n) = (-4)*(sqrt(3/7)*(((3-sqrt(21))/2)^n - ((3+sqrt(21))/2)^n)).

(End)

Example

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

Crossrefs

Column 1 of A238929.

Sequence in context: A191817 A270840 A064518 * A135178 A278583 A329859

Adjacent sequences: A238920 A238921 A238922 * A238924 A238925 A238926

Keyword

nonn

Author

R. H. Hardin, Mar 07 2014

Status

approved