A204748 Number of (n+2) X 4 0..1 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly three ways, and new values 0..1 introduced in row major order.

61, 46, 31, 28, 38, 49, 70, 106, 159, 248, 394, 625, 1002, 1614, 2599, 4196, 6782, 10961, 17726, 28674, 46383, 75040, 121410, 196433, 317826, 514246, 832055, 1346284, 2178326, 3524593, 5702902, 9227482, 14930367, 24157832, 39088186, 63246001

Offset

1,1

Comments

Column 2 of A204754.

Links

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

Formula

Empirical: a(n) = a(n-1) +a(n-2) +a(n-3) -a(n-4) -a(n-5) for n>8.

Empirical g.f.: x*(61 - 15*x - 76*x^2 - 110*x^3 - 6*x^4 + 59*x^5 + 32*x^6 + 8*x^7) / ((1 - x)*(1 - x - x^2)*(1 + x + x^2)). - Colin Barker, Jun 09 2018

Example

Some solutions for n=3:
..0..0..0..0....0..1..1..1....0..0..1..1....0..0..0..0....0..0..0..0
..0..0..0..0....0..0..1..1....0..0..1..1....1..1..1..1....1..1..1..1
..1..1..1..1....0..0..0..1....0..0..1..1....1..1..1..1....0..0..0..0
..0..0..0..0....1..0..0..0....0..0..1..1....0..0..0..0....1..1..1..1
..1..1..1..1....1..1..0..0....0..0..1..1....1..1..1..1....0..0..0..0

Crossrefs

Cf. A204754.

Sequence in context: A199749 A303687 A033381 * A276471 A122568 A075028

Adjacent sequences: A204745 A204746 A204747 * A204749 A204750 A204751

Keyword

nonn

Author

R. H. Hardin, Jan 18 2012

Status

approved