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A214387 Number of 5 X 5 X 5 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 A214387 #6 Sep 03 2022 21:34:12
%S A214387 32,11700,445024,6981540,65905056,444106514,2347567992,10319444960,
%T A214387 39220393240,132463100966,405642373936,1143607220512,3003599167616,
%U A214387 7418663549468,17363308642608,38750311281936,82891561168528
%N A214387 Number of 5 X 5 X 5 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 A214387 Row 5 of A214384.
%H A214387 R. H. Hardin, <a href="/A214387/b214387.txt">Table of n, a(n) for n = 1..33</a>
%F A214387 Empirical: a(n) = (250321/163459296000)*n^15 + (57931/605404800)*n^14 + (5905981/2335132800)*n^13 + (63247/1710720)*n^12 + (294798431/898128000)*n^11 + (9968141/5443200)*n^10 + (367113701/57153600)*n^9 + (34853713/2540160)*n^8 + (2644103053/163296000)*n^7 + (1285847/194400)*n^6 - (1094962783/179625600)*n^5 - (22292609/2993760)*n^4 - (316949617/252252000)*n^3 + (47012731/37837800)*n^2 + (3659/9009)*n.
%e A214387 Some solutions for n=3
%e A214387 ......0..........0..........2..........0..........0..........0..........0
%e A214387 .....2.0........0.1........1.2........0.2........0.3........0.2........0.2
%e A214387 ....3.0.2......2.0.2......0.2.1......3.0.2......1.0.3......0.1.2......0.3.1
%e A214387 ...1.3.0.2....2.1.0.2....0.1.3.1....3.0.3.2....1.0.2.3....0.1.0.2....3.0.3.1
%e A214387 ..0.3.2.0.2..0.3.1.0.2..0.1.3.2.0..1.3.0.3.2..1.2.0.3.0..0.2.0.2.1..3.0.3.0.2
%Y A214387 Cf. A214384.
%K A214387 nonn
%O A214387 1,1
%A A214387 _R. H. Hardin_, Jul 14 2012