A207165 Number of n X 4 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 0 1 vertically.

9, 81, 261, 603, 1161, 1989, 3141, 4671, 6633, 9081, 12069, 15651, 19881, 24813, 30501, 36999, 44361, 52641, 61893, 72171, 83529, 96021, 109701, 124623, 140841, 158409, 177381, 197811, 219753, 243261, 268389, 295191, 323721, 354033, 386181

Offset

1,1

Comments

Column 4 of A207169.

Links

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

Formula

Empirical: a(n) = 9*n^3 + 9*n - 9.

Conjectures from Colin Barker, Jun 19 2018: (Start)

G.f.: 9*x*(1 + 5*x - x^2 + x^3) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

(End)

Example

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

Crossrefs

Cf. A207169.

Sequence in context: A207786 A223189 A207781 * A208009 A207909 A208421

Adjacent sequences: A207162 A207163 A207164 * A207166 A207167 A207168

Keyword

nonn

Author

R. H. Hardin, Feb 15 2012

Status

approved