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%I #5 Mar 31 2012 12:36:24
%S 1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,3,15,1,1,1,1,3,18,135,1,1,1,1,3,
%T 18,228,2889,1,1,1,1,3,18,228,8472,146559,1,1,1,1,3,18,228,8904,
%U 898125,17742675,1,1,1,1,3,18,228,8904,1037343,276763188,5342155407,1,1,1,1,3
%N T(n,k)=Number of triangular nXnXn 0..k arrays with all row sums equal to the length of the row and all diagonal sums equal to the length of the respective diagonal
%C Table starts
%C .1........1.........1.........1.......1....1...1..1.1.1.1.1
%C .1........1.........1.........1.......1....1...1..1.1.1.1
%C .1........1.........1.........1.......1....1...1..1.1.1
%C .1........3.........3.........3.......3....3...3..3.3
%C .1.......15........18........18......18...18..18.18
%C .1......135.......228.......228.....228..228.228
%C .1.....2889......8472......8904....8904.8904
%C .1...146559....898125...1037343.1039761
%C .1.17742675.276763188.374504433
%H R. H. Hardin, <a href="/A195768/b195768.txt">Table of n, a(n) for n = 1..75</a>
%e Some solutions for n=8 k=6
%e .........1................1................1................1
%e ........0.2..............0.2..............0.2..............0.2
%e .......2.0.1............2.0.1............0.1.2............2.0.1
%e ......1.0.0.3..........1.0.2.1..........1.1.2.0..........1.1.1.1
%e .....1.2.1.1.0........1.0.2.2.0........0.2.1.1.1........1.0.0.2.2
%e ....0.1.1.0.4.0......2.2.1.1.0.0......3.1.1.0.1.0......1.1.2.0.2.0
%e ...2.2.2.1.0.0.0....0.1.0.0.1.3.2....2.0.0.1.2.1.1....1.2.2.2.0.0.0
%e ..1.0.1.0.0.3.2.1..1.2.0.1.3.0.0.1..1.0.0.3.0.2.1.1..1.1.0.0.0.3.2.1
%K nonn,tabl
%O 1,14
%A _R. H. Hardin_ Sep 23 2011
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