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A185858
1/128 the number of (n+2) X 3 binary arrays with no 3 X 3 subblock trace equal to any horizontal or vertical neighbor 3 X 3 subblock trace.
1
4, 22, 124, 694, 3892, 21814, 122284, 685462, 3842404, 21538774, 120736732, 676795894, 3793814164, 21266419702, 119210006284, 668237802454, 3745841266372, 20997505287574, 117702592547644, 659787917778742
OFFSET
1,1
COMMENTS
Column 1 of A185866.
LINKS
FORMULA
Empirical: a(n) = 4*a(n-1) + 9*a(n-2).
Conjectures from Colin Barker, Apr 17 2018: (Start)
G.f.: 2*x*(2 + 3*x) / (1 - 4*x - 9*x^2).
a(n) = ((2 - sqrt(13))^n*(-4+sqrt(13)) + (2+sqrt(13))^n*(4+sqrt(13))) / (3*sqrt(13)).
(End)
EXAMPLE
Some solutions for 4 X 3:
..0..0..0....1..0..0....0..1..1....0..0..0....0..0..1....0..1..0....1..0..0
..0..1..1....0..1..0....0..1..1....1..0..1....1..0..1....1..1..0....1..1..0
..0..0..1....0..0..1....0..1..0....0..0..0....0..1..1....0..1..0....0..0..1
..0..1..0....0..1..0....0..1..1....1..0..0....1..1..0....1..0..0....1..0..1
CROSSREFS
Cf. A185866.
Sequence in context: A065983 A236576 A375724 * A180034 A260346 A136777
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 05 2011
STATUS
approved