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.

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

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