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%I #4 Jul 14 2012 21:43:50
%S 16,890,11048,74260,350232,1305392,4107248,11363940,28412824,65439858,
%T 140806952,286079040,553378176,1025850192,1832212128,3166557496,
%U 5314833216,8689668506,13875533864,21686539292,33239546824,50045674976
%N Number of 4X4X4 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors, and no element equal to its horizontal neighbors
%C Row 4 of A214384
%H R. H. Hardin, <a href="/A214386/b214386.txt">Table of n, a(n) for n = 1..163</a>
%F Empirical: a(n) = (109/226800)*n^10 + (1531/90720)*n^9 + (6911/30240)*n^8 + (4553/3024)*n^7 + (27071/5400)*n^6 + (34159/4320)*n^5 + (409217/90720)*n^4 - (4937/4536)*n^3 - (22087/12600)*n^2 - (43/126)*n
%e Some solutions for n=3
%e .....3........2........2........2........2........3........2........2
%e ....3.2......1.2......3.0......2.3......2.1......2.3......0.2......1.2
%e ...1.3.0....0.1.2....3.2.0....0.3.2....2.1.2....1.3.0....0.1.2....0.3.2
%e ..0.1.3.0..1.0.3.2..3.0.3.0..0.1.3.1..2.0.1.3..0.3.0.2..0.2.1.2..0.2.3.0
%K nonn
%O 1,1
%A _R. H. Hardin_ Jul 14 2012
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