A183399 Half the number of n X 3 binary arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors.

4, 2, 6, 32, 110, 450, 1680, 6498, 24794, 95048, 364030, 1394450, 5342640, 20467202, 78415506, 300419072, 1150965830, 4409544050, 16893761040, 64722982898, 247965235594, 949998793608, 3639613683310, 13944005214050, 53421954623280

Offset

1,1

Comments

Column 3 of A183402.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 5*a(n-1) - 23*a(n-3) + 15*a(n-4) + 40*a(n-5) - 46*a(n-6) + 20*a(n-8) - 8*a(n-9) for n>10.

Empirical g.f.: 2*x*(2 - 9*x - 2*x^2 + 47*x^3 - 32*x^4 - 76*x^5 + 90*x^6 - 40*x^8 + 16*x^9) / ((1 - 5*x + 5*x^2 - 2*x^3)*(1 - 5*x^2 + 10*x^4 - 4*x^6)). - Colin Barker, Mar 28 2018

Example

Some solutions with a(1,1)=0 for 4 X 3:
..0..1..0....0..0..0....0..1..0....0..0..0....0..1..0....0..0..0....0..1..0
..1..1..0....1..1..1....0..1..0....1..1..1....0..1..0....1..1..1....0..1..1
..0..0..0....0..0..1....1..0..0....1..0..1....0..1..1....0..1..1....1..0..0
..1..1..1....1..0..1....1..0..1....1..0..1....0..0..0....0..0..0....1..0..1

Crossrefs

Cf. A183402.

Sequence in context: A132996 A019182 A019105 * A248250 A176385 A155829

Adjacent sequences: A183396 A183397 A183398 * A183400 A183401 A183402

Keyword

nonn

Author

R. H. Hardin, Jan 04 2011

Status

approved