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A198447
Number of 2n X 2 0..2 arrays with values 0..2 introduced in row major order and each element unequal to exactly two horizontal and vertical neighbors.
1
3, 13, 71, 433, 2763, 17941, 117263, 768313, 5038611, 33054493, 216872663, 1422982081, 9336876123, 61264171813, 401987528351, 2637661006153, 17307148601763, 113561761317421, 745141474228583, 4889285086978513
OFFSET
1,1
COMMENTS
Column 1 of A198452.
LINKS
FORMULA
Empirical: a(n) = 10*a(n-1) -25*a(n-2) +16*a(n-3).
Conjectures from Colin Barker, May 14 2018: (Start)
G.f.: x*(3 - 17*x + 16*x^2) / ((1 - x)*(1 - 9*x + 16*x^2)).
a(n) = 1/4 + (2^(-3-n)*((9+sqrt(17))^n*(-5+3*sqrt(17)) + (9-sqrt(17))^n*(5+3*sqrt(17)))) / sqrt(17).
(End)
EXAMPLE
Some solutions for n=3:
..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
..1..0....1..2....2..0....1..2....2..2....2..0....2..2....2..0....2..2....2..0
..1..0....1..2....2..0....1..2....1..1....2..0....1..1....2..0....1..1....2..0
..2..2....2..0....0..2....2..1....0..2....1..1....2..2....0..1....2..2....1..2
..1..1....2..0....0..2....2..1....0..2....2..2....1..1....0..1....0..0....1..2
..2..0....0..2....2..1....0..2....1..0....1..0....2..0....2..0....1..2....0..1
CROSSREFS
Cf. A198452.
Sequence in context: A227117 A277922 A182189 * A318223 A162326 A122455
KEYWORD
nonn
AUTHOR
R. H. Hardin, Oct 25 2011
STATUS
approved