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Number of n X 5 binary arrays without the pattern 0 0 0 antidiagonally or horizontally.
1

%I #7 Mar 17 2023 02:16:03

%S 24,576,11332,233756,4805140,98892196,2035428944,41894114820,

%T 862288002496,17748103310980,365301608074080,7518846739068100,

%U 154757206783943744,3185301402740998148,65561696535791184736

%N Number of n X 5 binary arrays without the pattern 0 0 0 antidiagonally or horizontally.

%C Column 5 of A188874.

%H R. H. Hardin, <a href="/A188870/b188870.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 24*a(n-1) -67*a(n-2) -48*a(n-3) -540*a(n-4) +2272*a(n-5) +1536*a(n-6) -6944*a(n-7) +2864*a(n-8) +1600*a(n-9) -768*a(n-10) for n>12.

%e Some solutions for 3 X 5

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

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

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

%Y Cf. A188874.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 12 2011