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

1,1

Comments

Column 3 of A204713.

Links

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

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)

Example

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

Crossrefs

Cf. A204713.

Sequence in context: A223181 A016814 A280343 * A174623 A100487 A157530

Adjacent sequences: A204705 A204706 A204707 * A204709 A204710 A204711

Keyword

nonn

Author

R. H. Hardin, Jan 18 2012

Status

approved