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A233020
Number of n X 2 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.
2
3, 15, 81, 435, 2337, 12555, 67449, 362355, 1946673, 10458075, 56183721, 301834755, 1621541217, 8711375595, 46799960409, 251422553235, 1350712686993, 7256408541435, 38983468081161, 209430157488675, 1125117723605697
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 5*a(n-1) + 2*a(n-2).
Conjectures from Colin Barker, Oct 06 2018: (Start)
G.f.: 3*x / (1 - 5*x - 2*x^2).
a(n) = sqrt(3/11)*(((5+sqrt(33))/2)^n - ((5-sqrt(33))/2)^n) = 3*A015535(n).
(End)
EXAMPLE
Some solutions for n=5:
..0..2....0..0....0..0....0..1....0..0....0..0....0..1....0..2....0..0....0..0
..2..2....1..1....2..2....1..1....1..1....0..2....0..1....2..0....1..1....0..0
..3..2....1..1....2..3....0..0....0..0....2..2....0..1....2..0....1..1....1..1
..3..2....1..3....3..3....2..2....1..1....2..3....0..1....0..2....3..3....3..1
..2..3....3..3....3..2....0..0....3..1....2..3....0..1....0..2....2..3....3..1
CROSSREFS
Column 2 of A233026.
Sequence in context: A003448 A229841 A198628 * A246020 A084120 A163470
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 03 2013
STATUS
approved