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%I
%S 3,6,21,36,63,90,129,168,219,270,333,396,471,546,633,720,819,918,1029,
%T 1140,1263,1386,1521,1656,1803,1950,2109,2268,2439,2610,2793,2976,
%U 3171,3366,3573,3780,3999,4218,4449,4680,4923,5166,5421,5676,5943,6210,6489
%N Number of 2X2X2 triangular 0..n arrays with some element plus some adjacent element totalling n+1 exactly once.
%C Row 2 of A270509.
%H R. H. Hardin, <a href="/A270510/b270510.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4)
%F Empirical for n mod 2 = 0: a(n) = 3*n^2 - 3*n
%F Empirical for n mod 2 = 1: a(n) = 3*n^2 - 3*n + 3
%e Some solutions for n=4
%e ...2....4....2....2....0....2....4....4....3....4....1....4....3....1....3....3
%e ..3.4..2.3..4.3..3.1..4.1..1.4..3.1..1.2..4.2..2.1..2.4..3.2..4.1..0.4..2.4..2.0
%Y Cf. A270509.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 18 2016
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