A202789 Number of n X 2 binary arrays with every one adjacent to another one horizontally, diagonally, antidiagonally or vertically.

2, 12, 50, 188, 724, 2820, 10960, 42544, 165176, 641376, 2490416, 9669968, 37547296, 145791744, 566092192, 2198069056, 8534842304, 33139784256, 128677866752, 499640952320, 1940046781312, 7532972421120, 29249641835776, 113572903188736

Offset

1,1

Comments

Column 2 of A202795.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 2*a(n-2) + 6*a(n-3).

Empirical g.f.: 2*x*(1 + 2*x + 3*x^2) / (1 - 4*x + 2*x^2 - 6*x^3). - Colin Barker, Mar 03 2018

Example

Some solutions for n=5:
  1 1   1 1   1 1   1 1   1 1   0 0   1 1   0 1   0 0   0 1
  0 0   0 1   1 1   1 0   1 1   1 0   0 1   1 1   1 1   0 1
  0 1   1 1   1 1   1 1   1 0   0 1   1 1   1 0   1 1   1 0
  1 0   1 0   0 1   0 0   1 0   1 0   0 1   0 0   1 1   0 0
  1 0   1 0   1 0   1 1   0 1   0 0   1 0   0 0   1 0   1 1

Crossrefs

Cf. A202795.

Sequence in context: A197891 A357782 A259802 * A129743 A115243 A218776

Adjacent sequences: A202786 A202787 A202788 * A202790 A202791 A202792

Keyword

nonn

Author

R. H. Hardin, Dec 24 2011

Status

approved