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A214386 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.

%I A214386 #6 Jul 22 2025 23:16:25
%S A214386 16,890,11048,74260,350232,1305392,4107248,11363940,28412824,65439858,
%T A214386 140806952,286079040,553378176,1025850192,1832212128,3166557496,
%U A214386 5314833216,8689668506,13875533864,21686539292,33239546824,50045674976
%N A214386 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 A214386 Row 4 of A214384
%H A214386 R. H. Hardin, <a href="/A214386/b214386.txt">Table of n, a(n) for n = 1..163</a>
%F A214386 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 A214386 Some solutions for n=3
%e A214386 .....3........2........2........2........2........3........2........2
%e A214386 ....3.2......1.2......3.0......2.3......2.1......2.3......0.2......1.2
%e A214386 ...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 A214386 ..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 A214386 nonn
%O A214386 1,1
%A A214386 _R. H. Hardin_ Jul 14 2012