A204751 Number of (n+2) X 7 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.

342, 38, 35, 40, 48, 61, 82, 116, 171, 260, 404, 637, 1014, 1624, 2611, 4208, 6792, 10973, 17738, 28684, 46395, 75052, 121420, 196445, 317838, 514256, 832067, 1346296, 2178336, 3524605, 5702914, 9227492, 14930379, 24157844, 39088196

Offset

1,1

Comments

Column 5 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*(342 - 646*x - 41*x^2 + 312*x^3 + 6*x^4) / ((1 - x)*(1 - x - x^2)). - Colin Barker, Jun 10 2018

Example

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

Crossrefs

Cf. A204754.

Sequence in context: A328665 A163582 A239271 * A247441 A045106 A137201

Adjacent sequences: A204748 A204749 A204750 * A204752 A204753 A204754

Keyword

nonn

Author

R. H. Hardin, Jan 18 2012

Status

approved