A183338 Number of n X 6 binary arrays with each 1 adjacent to exactly one 1 vertically and one 1 horizontally.

1, 9, 23, 51, 175, 513, 1397, 4133, 12075, 34521, 100047, 290287, 838039, 2423841, 7016381, 20290449, 58686583, 169784637, 491117363, 1420584719, 4109370831, 11887034385, 34384871493, 99464136973, 287716480627, 832264983105

Offset: 1

Author

R. H. Hardin, Jan 04 2011

Keywords

• nonn

Comments

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

Column 6 of A183342.

Examples

			Some solutions for 5 X 6:
  0 0 0 0 1 1   0 0 0 0 0 0   1 1 0 0 1 1   0 1 1 0 1 1
  1 1 0 0 1 1   0 0 1 1 0 0   1 1 0 0 1 1   0 1 1 0 1 1
  1 1 0 0 0 0   0 0 1 1 0 0   0 0 0 0 0 0   0 0 0 0 0 0
  0 0 1 1 0 0   1 1 0 0 1 1   0 0 0 0 0 0   0 0 0 1 1 0
  0 0 1 1 0 0   1 1 0 0 1 1   0 0 0 0 0 0   0 0 0 1 1 0
		

Links

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

Crossrefs

Cf. A183342.

Formula

Empirical: a(n) = a(n-1) + 2*a(n-2) + 9*a(n-3) + 6*a(n-4) - 3*a(n-5) - 10*a(n-6) - 17*a(n-7) - 7*a(n-8) + 12*a(n-9) + 12*a(n-10) - 6*a(n-11).

Empirical g.f.: x*(1 + 8*x + 12*x^2 + x^3 - 9*x^4 - 22*x^5 - 26*x^6 + 5*x^7 + 24*x^8 + 6*x^9 - 6*x^10) / (1 - x - 2*x^2 - 9*x^3 - 6*x^4 + 3*x^5 + 10*x^6 + 17*x^7 + 7*x^8 - 12*x^9 - 12*x^10 + 6*x^11). - Colin Barker, Mar 27 2018