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%I #5 Mar 31 2012 12:35:31
%S 1,12,82,469,2502,12966,66325,337222,1709652,8655795,43794966,
%T 221516992,1120277983,5665183308,28647552996,144861882889,
%U 732516467528,3704069018506,18730095418683,94711027286382,478917748054834
%N Number of nX3 binary arrays with all 1s connected and a path of 1s from left column to lower right corner
%H R. H. Hardin, <a href="/A163020/b163020.txt">Table of n, a(n) for n=1..100</a>
%F Empirical: a(n)= 10*a(n-1) -33*a(n-2) +45*a(n-3) -21*a(n-4) -15*a(n-5) +29*a(n-6) -9*a(n-7) -6*a(n-8) +a(n-9). G.f.: x*(-1-2*x+5*x^2+x^4+x^6)/((x-1) *(x^2+2*x-1) *(x^6-7*x^5+x^4+6*x^3-11*x^2+7* x-1) [From _R. J. Mathar_, Aug 11 2009]
%K nonn
%O 1,2
%A _R. H. Hardin_ Jul 20 2009
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