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Number of (n+2) X 4 binary arrays avoiding patterns 001 and 000 in rows and columns.
1

%I #12 Jun 01 2018 10:35:22

%S 510,3150,18160,107510,629790,3704980,21758550,127872530,751278240,

%T 4414434310,25937520830,152401930300,895465610130,5261491036130,

%U 30914921038320,181646780968570,1067301604632450,6271142423909740

%N Number of (n+2) X 4 binary arrays avoiding patterns 001 and 000 in rows and columns.

%C Column 2 of A202601.

%H R. H. Hardin, <a href="/A202595/b202595.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) +22*a(n-2) +12*a(n-3) -43*a(n-4) -8*a(n-5) +18*a(n-6) -a(n-8).

%F Empirical g.f.: 10*x*(51 + 213*x + 64*x^2 - 423*x^3 - 62*x^4 + 179*x^5 - x^6 - 10*x^7) / (1 - 2*x - 22*x^2 - 12*x^3 + 43*x^4 + 8*x^5 - 18*x^6 + x^8). - _Colin Barker_, Jun 01 2018

%e Some solutions for n=3:

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

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

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

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

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

%Y Cf. A202601.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 21 2011