A204377 Number of (n+2) X 6 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.

113, 63, 75, 87, 111, 153, 217, 323, 495, 771, 1219, 1945, 3117, 5015, 8087, 13055, 21095, 34105, 55153, 89211, 144319, 233483, 377755, 611193, 988901, 1600047, 2588903, 4188903, 6777759, 10966617, 17744329, 28710899, 46455183, 75166035

Offset

1,1

Comments

Column 4 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*(113 - 50*x - 101*x^2 - 164*x^3 - x^4 + 56*x^5 + 4*x^6 + 4*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..0..0..0....0..1..0..1..0..0....0..0..0..0..1..0....0..1..0..0..1..1
..0..1..1..0..0..1....0..1..0..1..0..0....1..1..1..1..1..1....0..1..0..0..1..1
..0..1..1..0..0..1....0..1..0..1..0..0....1..1..1..1..1..1....0..1..0..0..1..1
..0..1..1..0..0..1....0..1..0..1..0..0....0..1..0..0..0..0....0..1..0..0..1..1
..0..1..1..0..0..1....0..1..0..1..0..0....0..1..1..1..1..1....0..0..0..0..1..1

Crossrefs

Cf. A204381.

Sequence in context: A151645 A115486 A157885 * A242557 A345072 A214503

Adjacent sequences: A204374 A204375 A204376 * A204378 A204379 A204380

Keyword

nonn

Author

R. H. Hardin, Jan 14 2012

Status

approved