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A230179 Number of n X 3 0..2 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value 2-x(i,j).

%I A230179 #12 Feb 23 2025 11:20:51
%S A230179 3,27,231,1971,16815,143451,1223799,10440387,89068287,759853035,
%T A230179 6482404167,55302225363,471790411599,4024904802939,34336981580055,
%U A230179 292933215008739,2499051008758431,21319726218790923,181881331934084583
%N A230179 Number of n X 3 0..2 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value 2-x(i,j).
%H A230179 R. H. Hardin, <a href="/A230179/b230179.txt">Table of n, a(n) for n = 1..210</a>
%F A230179 Empirical: a(n) = 9*a(n-1) - 4*a(n-2).
%F A230179 Conjectures from _Colin Barker_, Sep 21 2018: (Start)
%F A230179 G.f.: 3*x / (1 - 9*x + 4*x^2).
%F A230179 a(n) = ((-3)*(2^(-n)*((9-sqrt(65))^n - (9+sqrt(65))^n))) / sqrt(65). (End)
%F A230179 Conjectured e.g.f.: 6*exp(9*x/2)*sinh(sqrt(65)*x/2)/sqrt(65). - _Stefano Spezia_, Feb 23 2025
%e A230179 Some solutions for n=3:
%e A230179 ..0..2..0....0..2..1....2..0..2....2..0..2....1..1..1....1..1..1....1..1..1
%e A230179 ..0..0..2....0..1..2....2..0..0....2..1..1....1..0..2....1..0..2....2..0..0
%e A230179 ..2..2..0....2..0..2....2..2..0....1..2..0....2..2..0....0..2..0....0..2..0
%Y A230179 Column 3 of A230184.
%K A230179 nonn
%O A230179 1,1
%A A230179 _R. H. Hardin_, Oct 11 2013