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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.
2

%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