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%I #10 May 05 2018 08:24:00
%S 7,17,41,95,219,493,1101,2427,5311,11529,24881,53399,114083,242725,
%T 514581,1087411,2291335,4815681,10097401,21126863,44117867,91963997,
%U 191384541,397682155,825190479,1710033273,3539371201,7317351687
%N Number of lower triangles of an (n+2) X (n+2) 0..2 array with new values introduced in row major order 0..2 and no element unequal to more than one horizontal or vertical neighbor.
%C Column 2 of A194778.
%H R. H. Hardin, <a href="/A194772/b194772.txt">Table of n, a(n) for n = 1..34</a>
%F Empirical: a(n) = 3*a(n-1) +a(n-2) -7*a(n-3) +4*a(n-5).
%F Conjectures from _Colin Barker_, May 05 2018: (Start)
%F G.f.: x*(7 - 4*x - 17*x^2 + 4*x^3 + 12*x^4) / ((1 - x)*(1 + x)^2*(1 - 2*x)^2).
%F a(n) = (-3*n + 2^(n+3)*(3*n+8) + 17) / 27 for n even.
%F a(n) = (3*n + 2^(n+3)*(3*n+8) + 10) / 27 for n odd.
%F (End)
%e All solutions for 3 X 3 including a 2.
%e ..0
%e ..1.1
%e ..1.1.2
%Y Cf. A194778.
%K nonn
%O 1,1
%A _R. H. Hardin_, Sep 02 2011
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