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A208089
Number of 8 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
216, 504, 1206, 3096, 7992, 20862, 54504, 142632, 373302, 977256, 2558376, 6697854, 17535096, 45907416, 120187062, 314653752, 823774104, 2156668542, 5646231432, 14782025736, 38699845686, 101317511304, 265252688136, 694440553086
OFFSET
1,1
COMMENTS
Row 7 of A208085.
LINKS
FORMULA
Empirical: a(n) = 3*a(n-1) - 3*a(n-3) + a(n-4).
Conjectures from Colin Barker, Jun 28 2018: (Start)
G.f.: 18*x*(12 - 8*x - 17*x^2 + 7*x^3) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)).
a(n) = (9/5)*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..0..1....0..0..0..1..0....0..1..0..0..1....0..0..0..1..1
..1..1..1..1..1....0..1..0..1..0....1..1..1..1..1....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..0..1..0..1....1..0..1..0..1....0..1..0..1..0....0..0..0..0..0
..0..1..0..1..0....0..1..0..1..0....1..0..1..0..1....0..0..0..0..0
..1..1..1..1..1....0..1..0..1..0....0..0..0..0..0....1..1..1..1..1
..1..1..1..1..1....1..0..1..0..1....0..0..0..0..0....1..1..1..1..1
..1..0..1..0..1....0..0..0..0..0....1..0..1..1..0....0..0..1..0..0
CROSSREFS
Cf. A208085.
Sequence in context: A043371 A304369 A074266 * A333316 A275154 A066890
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 23 2012
STATUS
approved