A204364 Number of (n+2) X 4 0..2 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..2 introduced in row major order.

212, 466, 673, 713, 1715, 4355, 11671, 31891, 86275, 235547, 643475, 1756499, 4798531, 13109875, 35813875, 97844819, 267317171, 730318259, 1995265651, 5451167539, 14892855091, 40688034995, 111161779763, 303699607091

Offset

1,1

Comments

Column 2 of A204370.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) -6*a(n-4) +4*a(n-6) for n>9.

Empirical g.f.: x*(212 - 170*x - 725*x^2 - 1306*x^3 + 848*x^4 + 2006*x^5 + 1796*x^6 - 708*x^7 - 1800*x^8) / ((1 - x)*(1 - 2*x - 2*x^2)*(1 - 2*x^3)). - Colin Barker, Jun 07 2018

Example

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

Crossrefs

Cf. A204370.

Sequence in context: A251126 A078211 A158794 * A235180 A353139 A114880

Adjacent sequences: A204361 A204362 A204363 * A204365 A204366 A204367

Keyword

nonn

Author

R. H. Hardin, Jan 14 2012

Status

approved