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A185761
Number of (n+1) X 2 binary arrays with no 2 X 2 subblock trace equal to any horizontal or vertical neighbor 2 X 2 subblock trace.
3
16, 40, 104, 264, 680, 1736, 4456, 11400, 29224, 74824, 191720, 491016, 1257896, 3221960, 8253544, 21141384, 54155560, 138721096, 355343336, 910227720, 2331601064, 5972511944, 15298916200, 39188963976, 100384628776, 257140484680
OFFSET
1,1
COMMENTS
Column 1 of A185769.
LINKS
FORMULA
Empirical: a(n) = a(n-1) + 4*a(n-2).
Conjectures from Colin Barker, Feb 22 2018: (Start)
G.f.: 8*x*(2 + 3*x) / (1 - x - 4*x^2).
a(n) = (2^(-n)*((1-sqrt(17))^n*(-13+3*sqrt(17)) + (1+sqrt(17))^n*(13+3*sqrt(17)))) / sqrt(17).
(End)
EXAMPLE
Some solutions for 3 X 2:
..0..1....0..0....1..1....0..0....1..1....1..1....1..0....0..0....0..1....1..1
..1..0....0..1....0..0....0..0....0..1....0..1....0..1....0..0....1..1....1..1
..1..1....1..0....1..0....1..1....0..1....1..1....0..0....0..1....1..1....0..0
CROSSREFS
Cf. A185769.
Sequence in context: A205065 A368078 A185790 * A205248 A205186 A197903
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 03 2011
STATUS
approved