_R. H. Hardin (rhhardin(AT)att.net) _ Aug 03 2009

Empirical: a(n)=A006355(n+7)-n^2-7n-17. G.f.: x*(1+3*x-2*x^2+x^4-x^3)/((x^2+x-1)*(x-1)^3). [From _R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, Aug 11 2009]

R. H. Hardin, <a href="/A163723/b163723.txt">Table of n, a(n) for n=1..100</a>

nonn,new

nonn

nonn,new

nonn

Ron R. H. Hardin (rhhardin(AT)att.net) Aug 03 2009

Number of nX2 binary arrays with all 1s connected, a path of 1s from left column to right column, and no 1 having more than two 1s adjacent

1, 7, 21, 49, 101, 193, 351, 617, 1059, 1787, 2979, 4923, 8085, 13219, 21545, 35037, 56889, 92269, 149539, 242229, 392231, 634967, 1027751, 1663319, 2691721, 4355743, 7048221, 11404777, 18453869, 29859577, 48314439, 78175073, 126490635

1,2

R. H. Hardin, <a href="b163723.txt">Table of n, a(n) for n=1..100</a>

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

Empirical: a(n)=A006355(n+7)-n^2-7n-17. G.f.: x*(1+3*x-2*x^2+x^4-x^3)/((x^2+x-1)*(x-1)^3). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 11 2009]

All solutions for n=3

...1.1...1.1...1.1...1.1...1.1...0.0...0.0...0.0...0.0...1.0...0.0...0.0...0.1

...0.0...0.1...1.0...1.1...1.0...0.0...0.1...1.0...1.1...1.0...1.1...1.1...1.1

...0.0...0.0...0.0...0.0...1.0...1.1...1.1...1.1...1.1...1.1...0.0...0.1...0.0

------

...0.0...0.1...1.0...1.0...1.1...1.1...0.1...1.1

...1.1...1.1...1.1...1.1...0.1...1.0...0.1...0.1

...1.0...1.0...0.0...0.1...0.1...1.1...1.1...1.1

nonn

Ron Hardin (rhhardin(AT)att.net) Aug 03 2009

approved