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%I #8 Jan 30 2019 06:21:10
%S 10,72,294,896,2268,5040,10164,19008,33462,56056,90090,139776,210392,
%T 308448,441864,620160,854658,1158696,1547854,2040192,2656500,3420560,
%U 4359420,5503680,6887790,8550360,10534482,12888064,15664176,18921408
%N Number of 3 X 3 X 3 triangular 0..n arrays with some element less than a w, nw or ne neighbor exactly once.
%H R. H. Hardin, <a href="/A271035/b271035.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/60)*n^6 + (7/30)*n^5 + (5/4)*n^4 + (19/6)*n^3 + (56/15)*n^2 + (8/5)*n.
%F Conjectures from _Colin Barker_, Jan 30 2019: (Start)
%F G.f.: 2*x*(5 + x) / (1 - x)^7.
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F (End)
%e Some solutions for n=4:
%e ....1......4......0......3......0......0......0......1......3......1......0
%e ...0.1....2.4....2.4....0.4....2.1....0.0....0.0....0.2....0.3....1.1....2.2
%e ..3.3.3..4.4.4..1.4.4..3.4.4..2.2.2..2.2.1..2.3.0..1.3.4..3.3.3..0.2.2..4.2.2
%Y Row 3 of A271034.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 29 2016
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