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Number of n X 1 0..2 arrays avoiding the patterns z z+1 z or z z-1 z in any row or column.
4

%I #9 Feb 20 2018 12:33:51

%S 3,9,23,61,161,425,1121,2957,7801,20581,54297,143245,377905,996981,

%T 2630217,6938989,18306305,48295333,127411801,336135325,886785649,

%U 2339500565,6172024649,16282914765,42957267425,113329023173,298982413497

%N Number of n X 1 0..2 arrays avoiding the patterns z z+1 z or z z-1 z in any row or column.

%C Column 1 of A207015.

%H R. H. Hardin, <a href="/A207008/b207008.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) - 2*a(n-2) + 2*a(n-3) + 2*a(n-4).

%F Empirical g.f.: x*(3 + 2*x^2 + 4*x^3) / (1 - 3*x + 2*x^2 - 2*x^3 - 2*x^4). - _Colin Barker_, Feb 20 2018

%e All solutions for n=4:

%e ..0....0....2....0....1....1....1....0....0....1....1....0....2....0

%e ..2....1....2....1....2....1....2....1....2....0....2....1....1....0

%e ..2....1....0....1....2....1....2....2....0....2....2....2....0....2

%e ..0....2....0....1....0....0....1....0....0....1....2....2....2....0

%Y Cf. A207015.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 14 2012