A204708 Number of (n+1) X 4 0..1 arrays with the permanents of all 2 X 2 subblocks equal and nonzero.

25, 81, 257, 833, 2689, 8705, 28161, 91137, 294913, 954369, 3088385, 9994241, 32342017, 104660993, 338690049, 1096024065, 3546808321, 11477712897, 37142659073, 120196169729, 388962975745, 1258710630401, 4073273163777

Offset: 1

Author

R. H. Hardin, Jan 18 2012

Keywords

• nonn

Comments

Column 3 of A204713.

Examples

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

Links

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

Crossrefs

Cf. A204713.

Formula

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

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

G.f.: x*(25 + 6*x - 36*x^2) / ((1 - x)*(1 - 2*x - 4*x^2)).

a(n) = (5 + (20-8*sqrt(5))*(1-sqrt(5))^n + 4*(1+sqrt(5))^n*(5+2*sqrt(5))) / 5.

(End)