A184679 Number of (n+1) X 3 binary arrays with every 2 X 2 subblock singular.

28, 128, 544, 2384, 10384, 45392, 198352, 867152, 3791056, 16575056, 72469456, 316854608, 1385372368, 6057228368, 26483886544, 115794964304, 506288081104, 2213633766992, 9678629263312, 42317689343312, 185024841512656

Offset

1,1

Comments

Column 2 of A184686.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 12*a(n-3).

Conjectures from Colin Barker, Apr 14 2018: (Start)

G.f.: 4*x*(7 - 3*x - 24*x^2) / ((1 - 2*x)*(1 - 3*x - 6*x^2)).

a(n) = 2^(-2-n)*(11*2^(1+2*n) - 3*(3-sqrt(33))^n*(-55+7*sqrt(33)) + 3*(3+sqrt(33))^n*(55+7*sqrt(33))) / 11.

(End)

Example

Some solutions for 5 X 3:
..0..0..1....1..0..1....1..0..1....0..0..0....0..0..1....0..0..0....0..0..1
..0..0..0....1..0..0....1..0..0....0..1..1....0..0..1....1..0..1....1..0..0
..0..0..1....0..0..0....0..0..0....0..0..0....0..0..1....0..0..1....0..0..0
..1..0..0....0..0..0....0..1..1....0..0..1....0..0..0....1..0..1....0..1..1
..1..0..0....0..0..0....0..0..0....1..0..1....1..0..1....1..0..0....0..0..0

Crossrefs

Cf. A184686.

Sequence in context: A044360 A044741 A318778 * A123376 A192796 A124956

Adjacent sequences: A184676 A184677 A184678 * A184680 A184681 A184682

Keyword

nonn

Author

R. H. Hardin, Jan 19 2011

Status

approved