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Number of n X 3 binary arrays without the pattern 0 0 diagonally or vertically.
1

%I #10 Apr 28 2018 08:11:23

%S 8,21,90,304,1141,4084,14925,54049,196508,713225,2590574,9406448,

%T 34159833,124045128,450458681,1635781681,5940155616,21570956189,

%U 78332387394,284454730240,1032963629229,3751084683708,13621618755397

%N Number of n X 3 binary arrays without the pattern 0 0 diagonally or vertically.

%C Column 3 of A188706.

%H R. H. Hardin, <a href="/A188700/b188700.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = a(n-1) + 8*a(n-2) + 6*a(n-3) - a(n-4) - a(n-5).

%F Empirical g.f.: x*(8 + 13*x + 5*x^2 - 2*x^3 - x^4) / ((1 + x)*(1 - 2*x - 6*x^2 + x^4)). - _Colin Barker_, Apr 28 2018

%e Some solutions for 4 X 3:

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

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

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

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

%Y Cf. A188706.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 08 2011