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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A212707 A267370 A213388 * A028345 A341985 A341066

Adjacent sequences:  A163712 A163713 A163714 * A163716 A163717 A163718

KEYWORD

nonn

AUTHOR

R. H. Hardin, Aug 03 2009

STATUS

approved

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Last modified June 27 13:59 EDT 2022. Contains 354896 sequences. (Running on oeis4.)