A254847 Number of (n+2) X (1+2) 0..1 arrays with no 3 x 3 subblock diagonal sum one and no antidiagonal sum two.

192, 576, 1632, 4624, 13328, 38416, 110544, 318096, 913680, 2624400, 7549200, 21715600, 62425360, 179452816, 515960336, 1483482256, 4265261840, 12263347600, 35258287120, 101370918544, 291456195856, 837979129744, 2409294812688

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-1) + 8*a(n-3) + 12*a(n-4) + 20*a(n-5) + 32*a(n-6) - 64*a(n-8) - 64*a(n-9)

Empirical g.f.: 16*x*(12 + 24*x + 66*x^2 + 91*x^3 + 112*x^4 + 80*x^5 - 132*x^6 - 352*x^7 - 256*x^8) / ((1 + 2*x^2 - 4*x^3)*(1 + 2*x^2 + 4*x^3)*(1 - x - 4*x^2 - 4*x^3)). - Colin Barker, Dec 18 2018

Example

Some solutions for n=4:
..0..0..0....1..1..0....0..1..0....1..1..1....0..1..0....1..0..0....1..0..1
..1..1..1....1..0..1....0..0..1....0..0..1....0..0..1....1..1..1....0..1..0
..0..1..1....1..1..1....0..1..0....0..1..1....0..0..0....0..0..1....1..0..1
..1..1..1....1..1..1....1..0..1....1..0..1....0..0..0....0..0..1....0..1..0
..1..0..1....1..1..0....0..1..0....0..1..0....0..1..0....0..0..0....1..0..0
..0..0..1....1..1..1....1..1..0....1..1..0....0..1..1....0..0..0....0..0..0

Crossrefs

Column 1 of A254854.

Sequence in context: A229361 A232940 A254854 * A251083 A336944 A194647

Adjacent sequences: A254844 A254845 A254846 * A254848 A254849 A254850

Keyword

nonn

Author

R. H. Hardin, Feb 08 2015

Status

approved