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A183278 Half the number of n X n X n triangular binary arrays with no array-aligned 2 X 2 X 2 subtriangle being all zero or all one.

%I A183278 #8 Feb 26 2015 08:42:08
%S A183278 1,3,13,80,693,8407,142362,3357612,110120153,5016480073,317135545779,
%T A183278 27803984036400,3378700619148221,568830517952061132,
%U A183278 132632829107728951932,42817890108690930718624
%N A183278 Half the number of n X n X n triangular binary arrays with no array-aligned 2 X 2 X 2 subtriangle being all zero or all one.
%H A183278 R. H. Hardin, <a href="/A183278/b183278.txt">Table of n, a(n) for n = 1..20</a>
%e A183278 Some solutions for 6X6X6 with a(1,1)=0
%e A183278 .......0............0............0............0............0............0
%e A183278 ......0.1..........0.1..........1.1..........1.1..........1.1..........1.0
%e A183278 .....1.1.0........1.1.0........1.0.0........0.1.0........0.0.0........0.0.1
%e A183278 ....0.0.1.0......0.1.0.1......0.1.0.1......1.0.1.1......0.1.1.0......0.1.0.0
%e A183278 ...0.1.1.0.1....1.0.0.1.0....1.0.0.1.0....0.1.0.1.0....0.1.0.1.0....1.0.0.1.1
%e A183278 ..1.0.0.1.1.0..0.0.1.0.1.0..0.0.1.0.1.0..1.0.1.0.1.1..1.1.0.1.0.1..1.0.1.0.1.0
%K A183278 nonn
%O A183278 1,2
%A A183278 _R. H. Hardin_, Jan 03 2011