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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
OFFSET
1,1
LINKS
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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jun 23 2015
STATUS
approved