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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 1 of A185769.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..200

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: A182461 A205065 A185790 * A205248 A205186 A197903

Adjacent sequences:  A185758 A185759 A185760 * A185762 A185763 A185764

KEYWORD

nonn

AUTHOR

R. H. Hardin, Feb 03 2011

STATUS

approved

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Last modified November 18 07:22 EST 2019. Contains 329252 sequences. (Running on oeis4.)