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%I #7 Feb 26 2018 19:24:14
%S 1,4,12,30,64,122,218,364,579,886,1310,1880,2636,3614,4862,6434,8387,
%T 10784,13704,17220,21422,26408,32280,39148,47143,56388,67028,79218,
%U 93118,108898,126754,146872,169465,194758,222982,254380,289226,327782,370342
%N Number of 5 X 5 X 5 triangular nonnegative integer arrays, symmetric under 120 degree rotation, with all sums of an element and its neighbors <= n.
%H R. H. Hardin, <a href="/A166213/b166213.txt">Table of n, a(n) for n=0..63</a>
%F Conjectures from _Colin Barker_, Feb 26 2018: (Start)
%F G.f.: (1 + 2*x + 3*x^2 + 4*x^3 + 3*x^4) / ((1 - x)^6*(1 + x)^2*(1 + x + x^2)^2).
%F a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - 3*a(n-4) + 6*a(n-6) - 3*a(n-8) - 2*a(n-9) + a(n-10) + 2*a(n-11) - a(n-12) for n>11.
%F (End)
%K nonn
%O 0,2
%A _R. H. Hardin_, Oct 09 2009