Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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