A206111 Number of (n+1) X 2 0..3 arrays with every 2 X 3 or 3 X 2 subblock having exactly two counterclockwise and two clockwise edge increases.

256, 1140, 6028, 31756, 171564, 973388, 5538732, 31668844, 182723180, 1055476940, 6101167404, 35321975916, 204551559276, 1184692892236, 6863075460012, 39761220992620, 230360296104556, 1334668498415052, 7732945730535980

Offset

1,1

Comments

Column 1 of A206118.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) + 5*a(n-2) + 29*a(n-3) - 142*a(n-4) - 248*a(n-5) + 88*a(n-6) + 144*a(n-7).

Empirical g.f.: 4*x*(64 - 35*x - 238*x^2 - 2877*x^3 - 3516*x^4 + 1836*x^5 + 2304*x^6) / ((1 - 2*x - 4*x^2)*(1 - 3*x - 7*x^2 - 55*x^3 + 4*x^4 + 36*x^5)). - Colin Barker, Jun 13 2018

Example

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

Crossrefs

Cf. A206118.

Sequence in context: A237299 A237293 A206118 * A237211 A237204 A237007

Adjacent sequences: A206108 A206109 A206110 * A206112 A206113 A206114

Keyword

nonn

Author

R. H. Hardin, Feb 03 2012

Status

approved