%I #8 Mar 21 2018 09:38:20
%S 1,3,8,21,53,132,323,783,1880,4485,10637,25116,59075,138519,323936,
%T 755877,1760453,4093620,9506051,22049055,51091496,118287237,273658877,
%U 632714892,1462080131,3377002023,7796796848,17994911781,41519520053
%N Number of n X 1 0..2 arrays with every repeated value in every row and column one larger mod 3 than the previous repeated value, and upper left element zero.
%C Column 1 of A267952.
%H R. H. Hardin, <a href="/A267946/b267946.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) + a(n-2) - 6*a(n-3).
%F Conjectures from _Colin Barker_, Mar 21 2018: (Start)
%F G.f.: x*(1 - 2*x^2) / ((1 - 2*x)*(1 - x - 3*x^2)).
%F a(n) = 2^(-n)*(-39*4^n + (26-7*sqrt(13))*(1-sqrt(13))^n + (1+sqrt(13))^n*(26+7*sqrt(13))) / 39.
%F (End)
%e Some solutions for n=8:
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..2....1....1....2....0....2....1....1....1....2....0....2....2....0....1....2
%e ..1....2....0....0....2....1....0....2....2....1....2....2....0....2....2....0
%e ..1....0....1....2....0....0....1....0....0....0....0....0....2....1....2....2
%e ..0....1....1....1....2....2....0....1....2....1....2....0....0....2....0....0
%e ..1....1....0....2....1....0....0....0....0....2....1....1....2....1....0....1
%e ..0....2....2....1....2....2....2....0....1....1....0....2....2....1....1....2
%e ..2....2....1....0....1....1....1....2....0....0....1....0....0....0....0....2
%Y Cf. A267952.
%K nonn
%O 1,2
%A _R. H. Hardin_, Jan 22 2016