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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.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 11 2014
STATUS
approved