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Number of nX1 0..2 arrays avoiding the pattern z-1 z-1 z in any row, column or nw-to-se diagonal
5

%I #7 Jul 17 2014 16:41:44

%S 3,9,25,69,190,523,1440,3965,10918,30064,82785,227959,627714,1728490,

%T 4759616,13106205,36089594,99377264,273647872,753524044,2074923809,

%U 5713565277,15733025007,43322875275,119295019315,328493931740

%N Number of nX1 0..2 arrays avoiding the pattern z-1 z-1 z in any row, column or nw-to-se diagonal

%C Column 1 of A206734

%H R. H. Hardin, <a href="/A206727/b206727.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) -2*a(n-3) +a(n-5).

%F Empirical: G.f.: -x*(3-2*x^2+x^4) / ( -1+3*x-2*x^3+x^5 ). - _R. J. Mathar_, Jul 17 2014

%e All solutions for n=4

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Feb 11 2012