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Number of 5X5X5 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors
1

%I #6 Jul 13 2012 06:40:11

%S 1386,80573,1602092,17790765,135538054,790197579,3766437036,

%T 15329961031,54922753470,177082458729,522464071332,1428914669655,

%U 3659885495134,8851607656183,20351858523224,44735107468453,94449669596498

%N Number of 5X5X5 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors

%C Row 5 of A214352

%H R. H. Hardin, <a href="/A214355/b214355.txt">Table of n, a(n) for n = 1..64</a>

%F Empirical: a(n) = (250321/163459296000)*n^15 + (57931/605404800)*n^14 + (6130183/2335132800)*n^13 + (5021701/119750400)*n^12 + (12225673/28066500)*n^11 + (33845911/10886400)*n^10 + (1793738911/114307200)*n^9 + (1441174417/25401600)*n^8 + (3431403169/23328000)*n^7 + (2949422359/10886400)*n^6 + (31221432373/89812800)*n^5 + (4515147647/14968800)*n^4 + (193448384201/1135134000)*n^3 + (4506398063/75675600)*n^2 + (2113313/180180)*n + 1

%e Some solutions for n=2

%e ......2..........2..........1..........1..........2..........1..........1

%e .....2.1........1.2........1.2........0.2........2.1........2.0........1.0

%e ....2.2.1......0.2.1......1.2.2......0.1.2......2.1.0......2.2.0......2.1.0

%e ...0.2.0.2....0.2.0.2....1.2.2.2....1.0.2.1....2.1.0.1....2.2.0.2....0.2.0.1

%e ..1.0.2.0.2..0.1.2.0.2..1.2.2.2.1..0.1.0.2.1..2.0.2.0.1..2.2.0.1.2..1.0.2.0.1

%K nonn

%O 1,1

%A _R. H. Hardin_ Jul 13 2012