%I #11 May 01 2019 14:04:09

%S 1,6,19,72,289,996,3325,11415,39720,138689,483837,1682961,5845649,

%T 20310166,70604782,245504404,853649448,2967979455,10318546476,

%U 35873587105,124720541039,433616480871,1507558685202,5241330944265

%N Number of n X 5 binary arrays with each 1 adjacent to exactly two other 1s.

%H R. H. Hardin, <a href="/A183326/b183326.txt">Table of n, a(n) for n = 1..200</a>

%H Robert Israel, <a href="/A183326/a183326.pdf">Maple-assisted proof of empirical g.f.</a>

%F Empirical: a(n)=5*a(n-1)-8*a(n-2)+9*a(n-3)-2*a(n-4)+14*a(n-5)+3*a(n-6)-44*a(n-7)+18*a(n-8)+29*a(n-9)-10*a(n-10)-69*a(n-11)+16*a(n-12)+87*a(n-13)+15*a(n-14)-55*a(n-15)-40*a(n-16)+6*a(n-17)+9*a(n-18)+4*a(n-19)-2*a(n-20).

%F Empirical formula verified (see link). - _Robert Israel_, May 01 2019

%e Some solutions for 7X5

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

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

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

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

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

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

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

%Y Column 5 of A183328.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 03 2011