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

Author

R. H. Hardin, Jan 18 2012

Keywords

• nonn

Comments

Column 2 of A204713.

Examples

			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
		

Links

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

Crossrefs

Cf. A204713.

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)