A208087 Number of 6 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.

72, 168, 402, 1032, 2664, 6954, 18168, 47544, 124434, 325752, 852792, 2232618, 5845032, 15302472, 40062354, 104884584, 274591368, 718889514, 1882077144, 4927341912, 12899948562, 33772503768, 88417562712, 231480184362

Offset

1,1

Comments

Row 5 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 27 2018: (Start)

G.f.: 6*x*(12 - 8*x - 17*x^2 + 7*x^3) / ((1 - x)*(1 + x)*(1 - 3*x + x^2)).

a(n) = (3/5)*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..1..1....0..0..0..0..1....0..0..1..0..1....0..0..0..1..0
..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..1..1..1..1....0..1..0..1..0....1..1..1..1..1
..1..0..1..0..1....0..1..0..1..0....0..0..0..0..0....1..0..1..0..1
..0..1..0..1..0....1..0..1..0..1....0..0..0..0..0....0..1..0..1..0
..0..0..0..0..0....0..0..1..1..1....1..0..1..0..1....1..1..0..1..0

Crossrefs

Cf. A208085.

Sequence in context: A044323 A044704 A302364 * A044404 A044785 A254437

Adjacent sequences: A208084 A208085 A208086 * A208088 A208089 A208090

Keyword

nonn

Author

R. H. Hardin, Feb 23 2012

Status

approved