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%I #4 Mar 24 2016 08:39:36
%S 0,0,30,270,1650,7344,24954,68838,164454,347916,677130,1219626,
%T 2083038,3373728,5268642,7918158,11590422,16482708,22978554,31322706,
%U 42040590,55422696,72165138,92600118,117625542,147608988,183683562,226243578
%N Number of 3X3X3 triangular 0..n arrays with some element plus some adjacent element totalling n+1, n or n-1 exactly once.
%C Row 3 of A270850.
%H R. H. Hardin, <a href="/A270852/b270852.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) for n>17
%F Empirical for n mod 2 = 0: a(n) = 27*n^5 - 531*n^4 + 4794*n^3 - 24417*n^2 + 69189*n - 86274 for n>7
%F Empirical for n mod 2 = 1: a(n) = 27*n^5 - 531*n^4 + 4806*n^3 - 24624*n^2 + 70425*n - 88833 for n>7
%e Some solutions for n=4
%e ....4......0......4......4......2......2......1......2......0......2......2
%e ...3.4....0.1....4.4....4.4....0.0....1.0....1.0....2.0....2.2....1.0....4.4
%e ..2.4.3..0.2.0..3.2.4..2.2.4..0.2.1..1.0.0..2.0.0..0.0.2..0.0.0..1.1.0..4.3.2
%Y Cf. A270850.
%K nonn
%O 1,3
%A _R. H. Hardin_, Mar 24 2016
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