A208086 Number of 4 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.

24, 56, 134, 344, 888, 2318, 6056, 15848, 41478, 108584, 284264, 744206, 1948344, 5100824, 13354118, 34961528, 91530456, 239629838, 627359048, 1642447304, 4299982854, 11257501256, 29472520904, 77160061454, 202007663448

Offset

1,1

Comments

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

a(n) = 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))) / 5.

(End)

Example

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

Crossrefs

Cf. A208085.

Sequence in context: A043198 A043978 A211461 * A232937 A190104 A255968

Adjacent sequences: A208083 A208084 A208085 * A208087 A208088 A208089

Keyword

nonn

Author

R. H. Hardin, Feb 23 2012

Status

approved