A208088 Number of 7 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.

108, 180, 288, 468, 756, 1224, 1980, 3204, 5184, 8388, 13572, 21960, 35532, 57492, 93024, 150516, 243540, 394056, 637596, 1031652, 1669248, 2700900, 4370148, 7071048, 11441196, 18512244, 29953440, 48465684, 78419124, 126884808

Offset

1,1

Comments

Row 6 of A208085.

Links

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

Formula

Empirical: a(n) = a(n-1) + a(n-2).

Conjectures from Colin Barker, Jun 27 2018: (Start)

G.f.: 36*x*(3 + 2*x) / (1 - x - x^2).

a(n) = (9*2^(2-n)*((1-sqrt(5))^n*(-2+sqrt(5)) + (1+sqrt(5))^n*(2+sqrt(5)))) / sqrt(5).

(End)

Example

Some solutions for n=4:
..0..0..0..1..0....0..1..0..1..1....0..0..0..0..0....0..0..0..1..0
..0..1..0..1..0....0..0..0..0..0....0..1..0..1..0....1..1..1..1..1
..1..0..1..0..1....0..0..0..0..0....1..0..1..0..1....1..1..1..1..1
..1..0..1..0..1....1..0..1..0..1....0..0..0..0..0....1..0..1..0..1
..0..1..0..1..0....0..1..0..1..0....0..0..0..0..0....0..1..0..1..0
..1..1..1..1..1....0..0..0..0..0....0..1..0..1..0....0..1..0..1..0
..1..1..1..1..1....0..0..0..0..0....1..0..1..0..1....1..0..1..0..1

Crossrefs

Cf. A208085.

Sequence in context: A039601 A330851 A245032 * A323548 A338382 A338384

Adjacent sequences: A208085 A208086 A208087 * A208089 A208090 A208091

Keyword

nonn

Author

R. H. Hardin, Feb 23 2012

Status

approved