A208064 Number of n X 3 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

6, 36, 72, 144, 216, 324, 432, 576, 720, 900, 1080, 1296, 1512, 1764, 2016, 2304, 2592, 2916, 3240, 3600, 3960, 4356, 4752, 5184, 5616, 6084, 6552, 7056, 7560, 8100, 8640, 9216, 9792, 10404, 11016, 11664, 12312, 12996, 13680, 14400, 15120, 15876, 16632

Offset

1,1

Comments

Column 3 of A208069.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>5.

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

G.f.: 6*x*(1 + 4*x + 2*x^3 - x^4) / ((1 - x)^3*(1 + x)).

a(n) = 9*n^2 for n>1 and even.

a(n) = 9*n^2-9 for n>1 and odd.

(End)

Example

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

Crossrefs

Cf. A208069.

Sequence in context: A161144 A364586 A119845 * A207929 A171506 A207683

Adjacent sequences: A208061 A208062 A208063 * A208065 A208066 A208067

Keyword

nonn

Author

R. H. Hardin, Feb 23 2012

Status

approved