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%I #3 Mar 31 2012 12:35:32
%S 1,3,17,186,3976,168568,14284278,2422957692,821682359716,
%T 556064922090416
%N Number of nXnXn triangular binary arrays with all 1s connected, and a path of 1s from peak vertex to anywhere on the bottom side
%e All solutions for n=3
%e ....1......1......1......1......1......1......1......1......1......1......1..
%e ...1.0....1.1....1.0....1.1....1.0....1.1....1.0....1.1....1.0....1.1....1.1.
%e ..0.1.0..0.1.0..1.1.0..1.1.0..0.1.1..0.1.1..1.1.1..1.1.1..1.0.0..1.0.0..1.0.1
%e ------
%e ....1......1......1......1......1......1..
%e ...0.1....0.1....0.1....0.1....0.1....1.1.
%e ..0.1.0..1.1.0..0.1.1..1.1.1..0.0.1..0.0.1
%K nonn
%O 1,2
%A _R. H. Hardin_ Aug 06 2009