A183326 Number of n X 5 binary arrays with each 1 adjacent to exactly two other 1s.

1, 6, 19, 72, 289, 996, 3325, 11415, 39720, 138689, 483837, 1682961, 5845649, 20310166, 70604782, 245504404, 853649448, 2967979455, 10318546476, 35873587105, 124720541039, 433616480871, 1507558685202, 5241330944265

Offset: 1

Author

R. H. Hardin, Jan 03 2011

Keywords

• nonn

Examples

			Some solutions for 7X5
..0..1..1..1..1....0..1..1..0..0....1..1..0..1..1....0..0..1..1..1
..1..1..0..0..1....0..1..1..0..0....1..1..0..1..1....1..1..1..0..1
..1..0..0..1..1....0..0..0..0..0....0..0..0..0..0....1..0..0..0..1
..1..0..0..1..0....0..0..1..1..1....0..1..1..1..0....1..1..0..1..1
..1..0..0..1..0....0..1..1..0..1....0..1..0..1..1....0..1..0..1..0
..1..1..0..1..0....0..1..0..1..1....0..1..0..0..1....0..1..0..1..0
..0..1..1..1..0....0..1..1..1..0....0..1..1..1..1....0..1..1..1..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200
• Robert Israel, Maple-assisted proof of empirical g.f.

Crossrefs

Column 5 of A183328.

Formula

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).

Empirical formula verified (see link). - Robert Israel, May 01 2019