%I #10 Jan 13 2023 14:42:15
%S 1,8,45,234,1193,6049,30616,154861,783150,3960215,20025500,101261654,
%T 512042141,2589202874,13092613725,66204360820,334770228305,
%U 1692805481383,8559872259604,43284012160451,218870755473698,1106746006355201,5596392811360844,28298825854292256
%N Number of n X 3 binary arrays with all 1s connected and a path of 1s from upper left corner to lower right corner.
%H R. H. Hardin, <a href="/A163003/b163003.txt">Table of n, a(n) for n=1..100</a>
%F From _R. J. Mathar_, Aug 11 2009: (Start)
%F Empirical: a(n) = 8*a(n1) 17*a(n2) +10*a(n3) +6*a(n4) 14*a(n5) +7*a(n6) +6*a(n7) a(n8).
%F Empirical g.f.: x*(1+x)*(x^4x^3+x^2+x1)/ ((x^2+x1)*(x^67*x^5+x^4+6*x^311*x^2+7*x1)). (End)
%F The above empirical formulas are correct.  _Andrew Howroyd_, Jan 06 2023
%Y Row 3 of A359573.
%K nonn
%O 1,2
%A _R. H. Hardin_, Jul 20 2009
