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A208087 Number of 6 X (n+1) 0..1 arrays with every 2 X 2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order. 1
72, 168, 402, 1032, 2664, 6954, 18168, 47544, 124434, 325752, 852792, 2232618, 5845032, 15302472, 40062354, 104884584, 274591368, 718889514, 1882077144, 4927341912, 12899948562, 33772503768, 88417562712, 231480184362 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Row 5 of A208085.
LINKS
FORMULA
Empirical: a(n) = 3*a(n-1) - 3*a(n-3) + a(n-4).
Conjectures from Colin Barker, Jun 27 2018: (Start)
G.f.: 6*x*(12 - 8*x - 17*x^2 + 7*x^3) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)).
a(n) = (3/5)*2^(1-n)*(2^n*(15+2*(-1)^n) + (9-4*sqrt(5))*(3-sqrt(5))^n + (3+sqrt(5))^n*(9+4*sqrt(5))).
(End)
EXAMPLE
Some solutions for n=4:
..0..1..0..1..1....0..0..0..0..1....0..0..1..0..1....0..0..0..1..0
..0..1..0..1..0....1..1..1..1..1....1..0..1..0..1....1..1..1..1..1
..1..0..1..0..1....1..1..1..1..1....0..1..0..1..0....1..1..1..1..1
..1..0..1..0..1....0..1..0..1..0....0..0..0..0..0....1..0..1..0..1
..0..1..0..1..0....1..0..1..0..1....0..0..0..0..0....0..1..0..1..0
..0..0..0..0..0....0..0..1..1..1....1..0..1..0..1....1..1..0..1..0
CROSSREFS
Cf. A208085.
Sequence in context: A044323 A044704 A302364 * A044404 A044785 A254437
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 23 2012
STATUS
approved

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Last modified April 12 20:17 EDT 2024. Contains 371636 sequences. (Running on oeis4.)