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%I #4 Jul 22 2012 07:44:36
%S 2,3,2,4,5,2,5,8,23,2,6,13,62,401,2,7,18,157,1862,20351,2,8,25,312,
%T 10177,187862,2869211,2,9,32,601,33352,3330677,63120962,1127599139,2,
%U 10,41,986,103651,20608352,5495329427,71200442882,1248252244661,2,11,50,1619
%N T(n,k)=Number of nXnXn triangular 0..k arrays with every horizontal row having the same average value
%C Table starts
%C .2.....3......4.......5........6.........7.........8..........9.........10
%C .2.....5......8......13.......18........25........32.........41.........50
%C .2....23.....62.....157......312.......601.......986.......1619.......2426
%C .2...401...1862...10177....33352....103651....250042.....589763....1199614
%C .2.20351.187862.3330677.20608352.121537201.493575042.1877543213.5767190924
%H R. H. Hardin, <a href="/A214595/b214595.txt">Table of n, a(n) for n = 1..1475</a>
%F Empirical for row n:
%F n=1: a(k)=2*a(k-1)-a(k-2)
%F n=2: a(k)=2*a(k-1)-2*a(k-3)+a(k-4)
%F n=3: (order 12 antisymmetric)
%F n=4: (order 32 symmetric)
%F n=5: (order 84 symmetric)
%e Some solutions for n=4 k=4
%e .....2........1........2........2........2........2........2........2
%e ....3.1......0.2......2.2......3.1......2.2......1.3......4.0......4.0
%e ...3.2.1....0.3.0....3.2.1....2.4.0....0.2.4....3.0.3....1.2.3....4.0.2
%e ..2.2.3.1..2.1.0.1..1.2.4.1..4.2.2.0..1.4.3.0..4.0.2.2..3.2.3.0..4.0.4.0
%Y Row 2 is A000982(n+1)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_ Jul 22 2012
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