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%I #4 Mar 20 2016 11:03:15
%S 0,0,312,1716,8148,23448,67788,144252,315936,568032,1049532,1692228,
%T 2793240,4176936,6369012,9014028,12965136,17596272,24205356,31786452,
%U 42217992,53986488,69705060,87206556,110011392,135134208,167193756
%N Number of 3X3X3 triangular 0..n arrays with some element plus some adjacent element totalling n+1 or n-1 exactly once.
%C Row 3 of A270606.
%H R. H. Hardin, <a href="/A270608/b270608.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) = 18*n^5 - 216*n^4 + 1296*n^3 - 4464*n^2 + 8562*n - 7188 for n>7
%F Empirical for n mod 2 = 1: a(n) = 18*n^5 - 216*n^4 + 1392*n^3 - 5532*n^2 + 13068*n - 14058 for n>7
%e Some solutions for n=4
%e ....3......4......1......3......1......1......4......3......3......4......3
%e ...4.3....4.0....1.0....3.4....3.3....2.0....2.3....3.3....2.4....4.4....4.0
%e ..0.3.1..3.3.1..0.1.3..3.1.3..0.1.3..4.2.0..2.4.3..2.4.3..0.2.4..2.3.3..0.0.0
%Y Cf. A270606.
%K nonn
%O 1,3
%A _R. H. Hardin_, Mar 20 2016
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