A204752 Number of (n+2) X 8 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.

590, 49, 48, 53, 61, 74, 95, 129, 184, 273, 417, 650, 1027, 1637, 2624, 4221, 6805, 10986, 17751, 28697, 46408, 75065, 121433, 196458, 317851, 514269, 832080, 1346309, 2178349, 3524618, 5702927, 9227505, 14930392, 24157857, 39088209

Offset

1,1

Comments

Column 6 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*(590 - 1131*x - 50*x^2 + 547*x^3 + 4*x^4) / ((1 - x)*(1 - x - x^2)). - Colin Barker, Jun 10 2018

Example

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

Crossrefs

Cf. A204754.

Sequence in context: A210894 A145699 A203628 * A320713 A116170 A171724

Adjacent sequences: A204749 A204750 A204751 * A204753 A204754 A204755

Keyword

nonn

Author

R. H. Hardin, Jan 18 2012

Status

approved