A204707 Number of (n+1) X 3 0..1 arrays with the permanents of all 2 X 2 subblocks equal and nonzero.

13, 33, 81, 209, 529, 1361, 3473, 8913, 22801, 58449, 149649, 383441, 982033, 2515793, 6443921, 16507089, 42282769, 108311121, 277442193, 710686673, 1820455441, 4663202129, 11945023889, 30597832401, 78377927953, 200769257553

Offset

1,1

Comments

Column 2 of A204713.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3).

Conjectures from Colin Barker, Jun 09 2018: (Start)

G.f.: x*(13 + 7*x - 24*x^2) / ((1 - x)*(1 - x - 4*x^2)).

a(n) = 1 + (2^(-1-n)*((1-sqrt(17))^n*(-19+5*sqrt(17)) + (1+sqrt(17))^n*(19+5*sqrt(17)))) / sqrt(17).

(End)

Example

Some solutions for n=4:
..1..0..1....0..1..0....1..1..1....0..1..1....1..1..0....0..1..1....0..1..1
..1..1..1....1..1..1....0..1..0....1..0..1....0..1..1....1..1..0....1..0..1
..1..0..1....1..0..1....1..1..1....1..1..0....1..0..1....0..1..1....1..1..1
..1..1..1....0..1..0....1..0..1....0..1..1....1..1..0....1..1..0....1..0..1
..1..0..1....1..1..1....0..1..1....1..1..0....0..1..1....1..0..1....0..1..1

Crossrefs

Cf. A204713.

Sequence in context: A024839 A146177 A146194 * A282686 A124659 A164539

Adjacent sequences: A204704 A204705 A204706 * A204708 A204709 A204710

Keyword

nonn

Author

R. H. Hardin, Jan 18 2012

Status

approved