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Number of 5X5X5 triangular 0..n arrays with every horizontal row nondecreasing, first elements of rows nonincreasing, last elements of rows nondecreasing, and every row having the same average value
1

%I #4 Aug 05 2012 06:17:27

%S 2,17,80,412,1558,5096,14826,39630,97184,223612,482160,991120,1946560,

%T 3679402,6713958,11870167,20399452,34184289,55959254,89708318,

%U 140988720,217682282,330552474,494354268,728865852,1060428048,1523781598

%N Number of 5X5X5 triangular 0..n arrays with every horizontal row nondecreasing, first elements of rows nonincreasing, last elements of rows nondecreasing, and every row having the same average value

%C Row 5 of A215182

%H R. H. Hardin, <a href="/A215185/b215185.txt">Table of n, a(n) for n = 1..147</a>

%e Some solutions for n=4

%e ......2..........1..........2..........3..........3..........2..........2

%e .....2.2........0.2........1.3........3.3........2.4........2.2........2.2

%e ....1.1.4......0.1.2......1.1.4......3.3.3......2.3.4......2.2.2......0.3.3

%e ...1.1.2.4....0.1.1.2....1.1.2.4....1.3.4.4....2.3.3.4....0.1.3.4....0.2.3.3

%e ..1.1.1.3.4..0.0.0.1.4..0.1.2.3.4..0.3.4.4.4..2.2.3.4.4..0.2.2.2.4..0.1.3.3.3

%K nonn

%O 1,1

%A _R. H. Hardin_ Aug 05 2012