A206248 Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having zero permanent.

49, 361, 1600, 9409, 47089, 258064, 1343281, 7198489, 37945600, 201895681, 1068570721, 5672499856, 30061664689, 159465247561, 845443470400, 4483691905729, 23774527583569, 126075439502224, 668536407557041

Offset

1,1

Comments

Column 1 of A206255.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) +12*a(n-2) -27*a(n-3).

a(n) = A006139(n+2)^2.

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

G.f.: x*(49 + 165*x - 432*x^2) / ((1 + 3*x)*(1 - 7*x + 9*x^2)).

a(n) = 2^(-n)*((-1)^n*2^(1+n)*3^(3+n) + (77-20*sqrt(13))*(7-sqrt(13))^n + (7+sqrt(13))^n*(77+20*sqrt(13))) / 13.

(End)

Example

Some solutions for n=4:
..1..0....2..1....2..1....2..3....2..3....3..3....3..3....0..3....0..3....0..1
..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..2....0..2....0..0
..0..3....1..0....2..1....2..3....0..0....1..1....3..1....0..3....0..0....0..1
..0..1....2..0....0..0....0..0....0..0....0..0....0..0....0..2....3..3....0..2
..0..3....1..0....3..0....1..3....3..0....1..1....0..1....0..1....0..0....0..2

Crossrefs

Cf. A206255.

Sequence in context: A269327 A206255 A017606 * A100690 A157882 A168572

Adjacent sequences: A206245 A206246 A206247 * A206249 A206250 A206251

Keyword

nonn

Author

R. H. Hardin, Feb 05 2012

Status

approved