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Number of 6X6X6 triangular 0..n arrays with some element plus some adjacent element totalling n+1 or n-1 exactly once.
1

%I #4 Mar 20 2016 11:05:55

%S 0,0,44168712,38923001616,1749723617976,176610474548304,

%T 4288332432901128,139782884096635692,1969237211896886586,

%U 29229202706222377392,264578668721400632640,2322718464029360624340,14967526923376689281208

%N Number of 6X6X6 triangular 0..n arrays with some element plus some adjacent element totalling n+1 or n-1 exactly once.

%C Row 6 of A270606.

%H R. H. Hardin, <a href="/A270611/b270611.txt">Table of n, a(n) for n = 1..14</a>

%e Some solutions for n=3

%e .......0............0............0............0............0............0

%e ......0.0..........0.0..........0.0..........0.0..........0.0..........0.0

%e .....0.1.0........0.3.0........3.0.3........3.0.0........0.1.0........3.0.0

%e ....0.0.0.0......3.0.1.0......0.3.3.0......0.3.0.0......0.0.3.0......0.3.3.0

%e ...0.0.0.0.1....0.0.0.0.0....0.0.3.3.3....0.0.0.0.3....0.0.3.0.0....0.0.0.3.3

%e ..0.0.0.3.0.3..0.0.1.0.0.0..0.0.0.0.0.1..0.0.0.0.1.0..0.0.3.3.0.0..0.0.1.0.0.1

%Y Cf. A270606.

%K nonn

%O 1,3

%A _R. H. Hardin_, Mar 20 2016