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%I #6 Mar 14 2016 09:20:40
%S 0,66,768,4428,14976,42750,96768,203448,376320,668250,1094400,1746756,
%T 2636928,3910998,5569536,7830000,10672128,14404338,18973440,24800700,
%U 31785600,40486446,50738688,63264168,77815296,95306250,115385088
%N Number of 3X3X3 triangular 0..n arrays with some element plus some adjacent element totalling n exactly once.
%C Row 3 of A270256.
%H R. H. Hardin, <a href="/A270258/b270258.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) +3*a(n-2) -8*a(n-3) -2*a(n-4) +12*a(n-5) -2*a(n-6) -8*a(n-7) +3*a(n-8) +2*a(n-9) -a(n-10)
%F Empirical for n mod 2 = 0: a(n) = 9*n^5 - 27*n^4 + 42*n^3 - 39*n^2 + 15*n
%F Empirical for n mod 2 = 1: a(n) = 9*n^5 - 27*n^4 + 30*n^3 + 6*n^2 - 39*n + 21
%e Some solutions for n=4
%e ....3......2......2......0......2......1......0......2......4......4......3
%e ...2.2....1.4....0.3....1.0....1.3....3.0....3.2....0.3....1.3....2.3....4.4
%e ..3.3.3..4.1.3..4.2.3..4.4.2..4.4.2..0.3.3..0.4.3..2.2.3..1.4.4..1.2.4..2.3.1
%Y Cf. A270256.
%K nonn
%O 1,2
%A _R. H. Hardin_, Mar 14 2016
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