A205066 Number of (n+1) X 3 0..1 arrays with the number of rightwards and downwards edge increases in each 2 X 2 subblock differing from the number in all its horizontal and vertical neighbors.

40, 64, 90, 146, 244, 386, 638, 1018, 1666, 2676, 4360, 7024, 11418, 18420, 29882, 48272, 78228, 126456, 204798, 331194, 536146, 867282, 1403624, 2270906, 3674698, 5945848, 9620410, 15567302, 25186452, 40757134, 65938814, 106705842, 172629762

Offset

1,1

Comments

Column 2 of A205072.

Links

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

Formula

Empirical: a(n) = 3*a(n-2) - a(n-6) - 4*a(n-8) - a(n-10) + a(n-12) for n > 14.

Empirical g.f.: 2*x*(20 + 32*x - 15*x^2 - 23*x^3 - 13*x^4 - 26*x^5 - 27*x^6 - 38*x^7 + x^8 + 12*x^9 + 3*x^10 + 15*x^11 + x^12 - 4*x^13) / ((1 + x - x^2)*(1 - x + x^2)*(1 - x - x^2)*(1 + x + x^2)*(1 - x^2 - x^4)). - Colin Barker, Jun 10 2018

Example

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

Crossrefs

Cf. A205072.

Sequence in context: A060672 A204754 A204747 * A232870 A338373 A355778

Adjacent sequences: A205063 A205064 A205065 * A205067 A205068 A205069

Keyword

nonn

Author

R. H. Hardin, Jan 21 2012

Status

approved