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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.
1
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
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 07 2014
STATUS
approved