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 A163686 Number of n X 3 binary arrays with all 1s connected, a path of 1s from upper left corner to lower right corner, and no 1 having more than two 1s adjacent. 1

%I

%S 1,5,17,39,83,175,375,807,1732,3690,7805,16441,34605,72893,153653,

%T 323917,682654,1438292,3030059,6383675,13449863,28338555,59708355,

%U 125801331,265051912,558439806,1176585241,2478972461,5223002977,11004454185

%N Number of n X 3 binary arrays with all 1s connected, a path of 1s from upper left corner to lower right corner, and no 1 having more than two 1s adjacent.

%H R. H. Hardin, <a href="/A163686/b163686.txt">Table of n, a(n) for n=1..56</a>

%F Empirical: a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 2*a(n-4) - 6*a(n-5) + 6*a(n-6) - 2*a(n-7) - a(n-8) + a(n-9) for n>=13.

%F Empirical g.f.: x*(1 + 2*x^2 - 6*x^3 + 10*x^4 - 4*x^5 - 2*x^6 + 4*x^7 + 6*x^8 + 2*x^9 - 3*x^10 - 2*x^11) / ((1 - x)^2*(1 - x + x^2 + x^3)*(1 - 2*x - x^4)). - _Colin Barker_, Mar 25 2018

%e All solutions for n=3:

%e ...1.0.0...1.0.0...1.0.0...1.0.0...1.1.0...1.1.0...1.1.1...1.1.1...1.1.0

%e ...1.1.0...1.1.1...1.0.0...1.0.1...1.0.0...1.0.1...1.0.0...1.0.1...0.1.0

%e ...0.1.1...0.0.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...0.1.1

%e ------

%e ...1.1.0...1.1.1...1.1.1...1.1.1...1.1.1...1.1.1...1.0.1...1.1.1

%e ...0.1.1...0.0.1...0.0.1...1.0.1...1.0.1...1.0.1...1.0.1...0.0.1

%e ...0.0.1...0.0.1...0.1.1...0.0.1...0.1.1...1.0.1...1.1.1...1.1.1

%K nonn

%O 1,2

%A _R. H. Hardin_, Aug 03 2009

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Last modified March 20 09:35 EDT 2023. Contains 361366 sequences. (Running on oeis4.)