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%I #3 Mar 31 2012 12:35:22
%S 252,2298,1670,5721,2507,7335,2348,4388,1087,1406,468,952,386,767,373,
%T 848,373,812,373,848,373,734,370,848,373,734,373,848,373,734,373,848,
%U 370,734,373,848,373,812,373,848,373,734,370,848,373,734,373,848,373,734,373
%N Number of planar triangular n X n X n nonnegative integer grids with mirror symmetry about one altitude with every similarly oriented 4 X 4 X 4 subtriangle summing to 9.
%e Maximal zeros solution for n=18
%e ...................1
%e ..................0.0
%e .................0.4.0
%e ................2.0.0.2
%e ...............0.0.3.0.0
%e ..............2.0.1.1.0.2
%e .............0.2.0.2.0.2.0
%e ............2.2.0.1.1.0.2.2
%e ...........0.0.1.0.3.0.1.0.0
%e ..........0.0.3.1.0.0.1.3.0.0
%e .........2.2.0.0.0.4.0.0.0.2.2
%e ........2.0.0.3.1.0.0.1.3.0.0.2
%e .......0.2.1.0.1.0.3.0.1.0.1.2.0
%e ......0.0.1.1.2.0.1.1.0.2.1.1.0.0
%e .....0.2.2.0.0.2.0.2.0.2.0.0.2.2.0
%e ....4.0.0.1.1.2.0.1.1.0.2.1.1.0.0.4
%e ...0.0.1.2.1.0.1.0.3.0.1.0.1.2.1.0.0
%e ..0.2.1.1.0.0.3.1.0.0.1.3.0.0.1.1.2.0
%K nonn
%O 4,1
%A _R. H. Hardin_ Jan 04 2009
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