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%I #16 Aug 07 2017 23:13:21
%S 1,3,4,18,51,266,1518,11396,111218,1345019,21178437,420441727,
%T 10691248879,346431341394,14306876354446,754052504644414
%N Number of n X n X n 0..6 triangular arrays with each element equal to the number its zero neighbors.
%C Also the number of maximal independent vertex sets (and minimal vertex covers) in the (n-1)-triangular grid graph. - _Eric W. Weisstein_, Jun 14 and Aug 07 2017
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimalVertexCover.html">Minimal Vertex Cover</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MaximalIndependentVertexSet.html">Maximal Independent Vertex Set</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TriangularGridGraph.html">Triangular Grid Graph</a>
%e Some solutions for 5 X 5 X 5:
%e ......1..........0..........0..........0..........0..........1..........0
%e .....1.0........2.2........1.2........2.1........1.2........0.2........2.2
%e ....1.2.2......0.2.0......1.1.0......0.1.1......1.1.0......1.2.0......1.0.1
%e ...0.2.0.2....2.2.2.2....0.2.2.2....2.2.1.0....0.1.2.2....1.1.1.2....1.2.2.1
%e ..1.1.1.2.0..0.2.0.2.0..1.2.0.2.0..1.0.1.1.1..1.1.1.0.1..1.0.1.1.0..0.2.0.2.0
%K nonn
%O 1,2
%A _R. H. Hardin_, Oct 16 2011