editing

approved

Number of nX5 n X 5 binary arrays with each 1 adjacent to exactly two other 1s.

Column 5 of A183328

Column 5 of A183328.

proposed

editing

editing

proposed

R. H. Hardin , Jan 03 2011

proposed

editing

editing

proposed

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

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

approved

editing

_R. H. Hardin (rhhardin(AT)att.net) _ Jan 03 2011

proposed

approved

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

allocated for Ron HardinNumber of nX5 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

1,2

Column 5 of A183328

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)

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

allocated

nonn

R. H. Hardin (rhhardin(AT)att.net) Jan 03 2011

approved

proposed