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

1,2

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Robert Israel, Maple-assisted proof of empirical g.f.

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

Example

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

Crossrefs

Column 5 of A183328.

Sequence in context: A266472 A259804 A060579 * A123950 A100191 A191585

Adjacent sequences: A183323 A183324 A183325 * A183327 A183328 A183329

Keyword

nonn

Author

R. H. Hardin, Jan 03 2011

Status

approved