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

Author

R. H. Hardin, Feb 23 2012

Keywords

• nonn

Comments

Row 7 of A208085.

Examples

			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
		

Links

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

Crossrefs

Cf. A208085.

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)