A239171 Number of (n+1) X (1+1) 0..2 arrays with no element greater than all horizontal neighbors or equal to all vertical neighbors.

6, 12, 36, 96, 264, 720, 1968, 5376, 14688, 40128, 109632, 299520, 818304, 2235648, 6107904, 16687104, 45590016, 124554240, 340288512, 929685504, 2539948032, 6939267072, 18958430208, 51795394560, 141507649536, 386606088192

Offset

1,1

Links

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

N. H. Bong, C. Dalfó, and M. À. Fiol, and D. Závacká, Some inner metric parameters of a digraph: Iterated line digraphs and integer sequences, arXiv:2409.02125 [math.CO], 2024. See p. 19.

Formula

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

Conjectures from Colin Barker, Oct 25 2018: (Start)

G.f.: 6*x / (1 - 2*x - 2*x^2).

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

(End)

Example

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

Crossrefs

Column 1 of A239178.

Sequence in context: A176681 A064476 A324483 * A264955 A038266 A298881

Adjacent sequences: A239168 A239169 A239170 * A239172 A239173 A239174

Keyword

nonn

Author

R. H. Hardin, Mar 11 2014

Status

approved