A204749 Number of (n+2) X 5 0..1 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly three ways, and new values 0..1 introduced in row major order.

102, 31, 22, 27, 35, 48, 69, 103, 158, 247, 391, 624, 1001, 1611, 2598, 4195, 6779, 10960, 17725, 28671, 46382, 75039, 121407, 196432, 317825, 514243, 832054, 1346283, 2178323, 3524592, 5702901, 9227479, 14930366, 24157831, 39088183

Offset

1,1

Comments

Column 3 of A204754.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - a(n-3) for n > 5.

Empirical g.f.: x*(102 - 173*x - 40*x^2 + 85*x^3 + 12*x^4) / ((1 - x)*(1 - x - x^2)). - Colin Barker, Jun 09 2018

Example

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

Crossrefs

Cf. A204754.

Sequence in context: A015164 A325776 A325775 * A244949 A266017 A144469

Adjacent sequences: A204746 A204747 A204748 * A204750 A204751 A204752

Keyword

nonn

Author

R. H. Hardin, Jan 18 2012

Status

approved