A183337 Number of n X 5 binary arrays with each 1 adjacent to exactly one 1 vertically and one 1 horizontally.

1, 6, 13, 26, 72, 175, 407, 1005, 2450, 5893, 14318, 34780, 84221, 204245, 495483, 1201256, 2912843, 7064014, 17129250, 41536473, 100724269, 244248135, 592280544, 1436238121, 3482767494, 8445435610, 20479537209, 49661306333, 120424822297

Offset

1,2

Comments

Equivalent to all 1s connected only in 2 X 2 blocks.

Column 5 of A183342.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = a(n-1) + a(n-2) + 5*a(n-3) + 2*a(n-4) + a(n-5) - a(n-7) - a(n-8).

Empirical g.f.: x*(1 + 5*x + 6*x^2 + 2*x^3 + x^4 - x^5 - 2*x^6 - x^7) / (1 - x - x^2 - 5*x^3 - 2*x^4 - x^5 + x^7 + x^8). - Colin Barker, Mar 27 2018

Example

Some solutions for 7 X 5:
  1 1 0 0 0    0 0 0 1 1    0 0 1 1 0    0 0 1 1 0
  1 1 0 0 0    0 0 0 1 1    0 0 1 1 0    0 0 1 1 0
  0 0 1 1 0    0 0 0 0 0    1 1 0 0 0    0 0 0 0 0
  0 0 1 1 0    0 0 0 0 0    1 1 0 0 0    1 1 0 1 1
  0 0 0 0 0    0 0 1 1 0    0 0 0 0 0    1 1 0 1 1
  1 1 0 0 0    0 0 1 1 0    0 0 0 1 1    0 0 0 0 0
  1 1 0 0 0    0 0 0 0 0    0 0 0 1 1    0 0 0 0 0

Crossrefs

Cf. A183342.

Sequence in context: A343007 A192762 A268721 * A358244 A301687 A173559

Adjacent sequences: A183334 A183335 A183336 * A183338 A183339 A183340

Keyword

nonn

Author

R. H. Hardin, Jan 04 2011

Status

approved