A163715 Number of n X 3 binary arrays with all 1s connected, a path of 1s from top row to bottom row, and no 1 having more than two 1s adjacent.

6, 21, 48, 108, 236, 506, 1080, 2294, 4854, 10248, 21614, 45564, 96028, 202354, 426376, 898374, 1892838, 3988096, 8402638, 17703724, 37300364, 78588906, 165580536, 348864886, 735030230, 1548649464, 3262879566, 6874624124

Offset

1,1

Comments

Same recurrence for A163696.

Same recurrence for A163734.

Links

R. H. Hardin, Table of n, a(n) for n=1..41

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) + a(n-4) - 2*a(n-5) + a(n-6) for n>=10.

Empirical g.f.: x*(1 + x)*(6 - 9*x + 3*x^2 + 6*x^3 - 10*x^4 + 7*x^5 + x^6 - 2*x^7) / ((1 - x)^2*(1 - 2*x - x^4)). - Colin Barker, Feb 22 2018

Example

All solutions for n=2:
...1.0.0...1.0.0...1.1.0...1.1.0...1.1.1...0.0.1...0.0.1...0.1.1...0.1.1
...1.0.0...1.1.0...1.0.0...1.1.0...1.0.0...0.0.1...0.1.1...0.0.1...0.1.1
------
...1.1.1...0.1.0...0.1.0...0.1.0...0.1.1...0.1.1...1.1.0...1.1.0...1.0.0
...0.0.1...0.1.0...0.1.1...1.1.0...0.1.0...1.1.0...0.1.0...0.1.1...1.1.1
------
...1.1.1...0.0.1...1.0.1
...1.0.1...1.1.1...1.1.1

Crossrefs

Sequence in context: A267370 A213388 A372226 * A028345 A357691 A341985

Adjacent sequences: A163712 A163713 A163714 * A163716 A163717 A163718

Keyword

nonn

Author

R. H. Hardin, Aug 03 2009

Status

approved