A183326 - OEIS

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

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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