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A259243 Number of (n+1) X (1+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0111. 1
9, 21, 48, 111, 255, 588, 1353, 3117, 7176, 16527, 38055, 87636, 201801, 464709, 1070112, 2464239, 5674575, 13067292, 30091017, 69292893, 159565944, 367444623, 846142455, 1948476324, 4486903689, 10332332661, 23793043728, 54790041711 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = a(n-1) + 3*a(n-2).

Conjectures from Colin Barker, Dec 24 2018: (Start)

G.f.: 3*x*(3 + 4*x) / (1 - x - 3*x^2).

a(n) = (2^(-n)*((1-sqrt(13))^n*(-7+2*sqrt(13)) + (1+sqrt(13))^n*(7+2*sqrt(13)))) / sqrt(13).

(End)

EXAMPLE

Some solutions for n=4:

..1..0....1..1....1..0....0..1....1..0....1..1....1..1....1..0....0..1....0..1

..1..0....1..0....1..1....1..1....1..1....0..1....0..1....1..1....1..1....1..1

..1..1....1..0....0..1....0..1....0..0....1..1....0..1....0..1....1..0....0..0

..0..0....1..1....1..1....1..1....1..1....0..1....1..1....1..1....1..1....1..1

..1..1....0..1....0..0....0..1....0..0....0..1....0..0....1..0....1..0....0..0

CROSSREFS

Column 1 of A259250.

Sequence in context: A246318 A277715 A173391 * A241747 A133762 A160414

Adjacent sequences:  A259240 A259241 A259242 * A259244 A259245 A259246

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jun 22 2015

STATUS

approved

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Last modified August 3 06:22 EDT 2021. Contains 346435 sequences. (Running on oeis4.)