A204295 Number of n X 2 0..3 arrays with every element neighboring horizontally or vertically both a 0 and a 1, and 2 introduced before 3 in row major order.

0, 4, 4, 16, 68, 212, 776, 3076, 11540, 44944, 177748, 700292, 2779272, 11069140, 44107780, 176038288, 703199588, 2809956020, 11232774920, 44913243940, 179603461748, 718287355024, 2872823053300, 11490415637348, 45959392743048

Offset

1,2

Comments

Column 2 of A204301.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) +2*a(n-2) +4*a(n-3) -42*a(n-4) -30*a(n-5) +13*a(n-6) +38*a(n-7) +28*a(n-8) -16*a(n-9).

Empirical g.f.: 4*x^2*(1 - 3*x - 2*x^2 - 5*x^3 + 15*x^4 + 4*x^5 + 4*x^6 - 8*x^7) / ((1 - x)*(1 + x)*(1 - 4*x)*(1 - 3*x + x^2)*(1 + x + x^2)*(1 + 2*x + 4*x^2)). - Colin Barker, Jun 07 2018

Example

Some solutions for n=5:
..0..0....0..1....0..1....1..1....0..0....1..0....0..1....0..1....1..0....0..0
..1..1....0..1....0..1....0..0....1..1....1..0....0..1....0..1....1..0....1..1
..0..0....2..1....1..1....2..1....0..1....0..1....2..0....0..1....1..0....0..2
..1..1....1..0....0..0....1..1....0..0....0..1....1..0....1..0....1..0....0..1
..0..0....1..0....1..1....0..0....1..1....0..1....1..0....1..0....1..0....0..1

Crossrefs

Cf. A204301.

Sequence in context: A203536 A038788 A010099 * A203101 A060691 A075225

Adjacent sequences: A204292 A204293 A204294 * A204296 A204297 A204298

Keyword

nonn

Author

R. H. Hardin, Jan 14 2012

Status

approved