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%I #4 Mar 18 2016 08:06:26
%S 15,144,1137,4584,15843,40392,95109,189936,362487,625440,1048665,
%T 1643544,2526027,3699864,5343213,7443552,10259679,13751856,18280257,
%U 23764680,30689715,38919144,49087317,60984144,75421383,92094912,112023849
%N Number of 3X3X3 triangular 0..n arrays with some element plus some adjacent element totalling n+1 exactly once.
%C Row 3 of A270509.
%H R. H. Hardin, <a href="/A270511/b270511.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 - 36*n^4 + 96*n^3 - 111*n^2 + 54*n
%F Empirical for n mod 2 = 1: a(n) = 9*n^5 - 36*n^4 + 108*n^3 - 156*n^2 + 132*n - 42
%e Some solutions for n=4
%e ....4......1......3......2......1......0......3......1......2......0......3
%e ...3.2....4.0....3.3....4.1....3.3....3.1....4.1....3.0....2.1....2.0....3.4
%e ..3.0.1..3.3.4..0.1.4..3.3.0..2.0.3..4.1.3..4.0.1..0.2.0..4.4.2..0.3.3..3.1.3
%Y Cf. A270509.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 18 2016
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