A207924 Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 0 and 1 1 1 vertically.

9, 81, 144, 576, 1936, 6400, 21904, 73984, 250000, 846400, 2862864, 9684544, 32764176, 110838784, 374964496, 1268499456, 4291298064, 14517358144, 49111878544, 166144281664, 562062085264, 1901442429184, 6432533627536

Offset

1,1

Comments

Column 4 of A207928.

It seems that all terms are squares. - Colin Barker, Mar 06 2018

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) + 6*a(n-3) - a(n-4) - a(n-6) for n>8.

Empirical g.f.: x*(9 + 63*x - 45*x^2 - 9*x^3 - 125*x^4 + 17*x^5 - 7*x^6 + 17*x^7) / ((1 + x + x^2 - x^3)*(1 - 3*x - x^2 - x^3)). - Colin Barker, Mar 06 2018

Example

Some solutions for n=8:
..0..1..1..0....1..0..0..1....1..0..0..1....1..0..1..1....0..1..1..0
..1..0..0..1....0..1..1..0....0..1..1..0....0..0..1..1....0..1..1..1
..1..1..1..1....1..0..1..1....0..0..1..1....1..1..0..0....1..0..0..1
..0..1..1..0....1..1..0..1....1..0..0..1....1..0..1..1....0..1..1..0
..1..0..0..1....0..1..1..0....1..1..0..0....0..0..1..1....0..1..1..1
..1..0..1..1....0..0..1..1....0..1..1..0....1..1..0..0....1..0..0..1
..0..1..1..0....1..1..0..1....0..0..1..1....1..0..1..1....1..1..1..0
..1..1..0..1....1..1..1..0....1..0..0..1....0..1..1..1....0..1..1..1

Crossrefs

Cf. A207928.

Sequence in context: A207695 A158028 A207591 * A343134 A343104 A043180

Adjacent sequences: A207921 A207922 A207923 * A207925 A207926 A207927

Keyword

nonn

Author

R. H. Hardin, Feb 21 2012

Status

approved