A204375 Number of (n+2) X 4 0..1 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically or nw-to-se diagonally exactly three ways, and new values 0..1 introduced in row major order.

51, 48, 54, 63, 88, 128, 193, 300, 470, 747, 1196, 1920, 3093, 4992, 8062, 13031, 21072, 34080, 55129, 89188, 144294, 233459, 377732, 611168, 988877, 1600024, 2588878, 4188879, 6777736, 10966592, 17744305, 28710876, 46455158, 75166011, 121621148

Offset

1,1

Comments

Column 2 of A204381.

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*(51 - 3*x - 45*x^2 - 90*x^3 - 26*x^4 + 22*x^5 + 16*x^6 + 8*x^7) / ((1 - x)*(1 - x - x^2)*(1 + x + x^2)). - Colin Barker, Jun 07 2018

Example

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

Crossrefs

Cf. A204381.

Sequence in context: A191514 A334339 A131536 * A003912 A039932 A210183

Adjacent sequences: A204372 A204373 A204374 * A204376 A204377 A204378

Keyword

nonn

Author

R. H. Hardin, Jan 14 2012

Status

approved