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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 7 of A208085.

LINKS

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

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

Adjacent sequences:  A208086 A208087 A208088 * A208090 A208091 A208092

KEYWORD

nonn

AUTHOR

R. H. Hardin, Feb 23 2012

STATUS

approved

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Last modified March 31 03:48 EDT 2020. Contains 333136 sequences. (Running on oeis4.)