|
%I #7 Sep 21 2018 11:49:47
%S 3,27,231,1971,16815,143451,1223799,10440387,89068287,759853035,
%T 6482404167,55302225363,471790411599,4024904802939,34336981580055,
%U 292933215008739,2499051008758431,21319726218790923,181881331934084583
%N 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 R. H. Hardin, <a href="/A230179/b230179.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 9*a(n-1) - 4*a(n-2).
%F Conjectures from _Colin Barker_, Sep 21 2018: (Start)
%F G.f.: 3*x / (1 - 9*x + 4*x^2).
%F a(n) = ((-3)*(2^(-n)*((9-sqrt(65))^n - (9+sqrt(65))^n))) / sqrt(65).
%F (End)
%e Some solutions for n=3:
%e ..0..2..0....0..2..1....2..0..2....2..0..2....1..1..1....1..1..1....1..1..1
%e ..0..0..2....0..1..2....2..0..0....2..1..1....1..0..2....1..0..2....2..0..0
%e ..2..2..0....2..0..2....2..2..0....1..2..0....2..2..0....0..2..0....0..2..0
%Y Column 3 of A230184.
%K nonn
%O 1,1
%A _R. H. Hardin_, Oct 11 2013
| 