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A259290 Number of (n+1) X (1+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0001 0101 or 0111. 1
10, 26, 66, 170, 434, 1114, 2850, 7306, 18706, 47930, 122754, 314474, 805490, 2063386, 5285346, 13538890, 34680274, 88835834, 227556930, 582900266, 1493127986, 3824729050, 9797240994, 25096157194, 64285121170, 164669749946 (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) + 4*a(n-2).

Conjectures from Colin Barker, Dec 25 2018: (Start)

G.f.: 2*x*(5 + 8*x) / (1 - x - 4*x^2).

a(n) = (2^(1-n)*((1-sqrt(17))^n*(-4+sqrt(17)) + (1+sqrt(17))^n*(4+sqrt(17)))) / sqrt(17).

(End)

EXAMPLE

Some solutions for n=4:

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

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

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

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

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

CROSSREFS

Column 1 of A259297.

Sequence in context: A332596 A134420 A144255 * A072379 A005970 A192254

Adjacent sequences:  A259287 A259288 A259289 * A259291 A259292 A259293

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jun 23 2015

STATUS

approved

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Last modified April 4 07:32 EDT 2020. Contains 333213 sequences. (Running on oeis4.)