A206112 Number of (n+1) X 3 0..3 arrays with every 2 X 3 or 3 X 2 subblock having exactly two counterclockwise and two clockwise edge increases.

1140, 5228, 22624, 111552, 588840, 3048096, 16072760, 84203240, 442219464, 2322616208, 12190484896, 64028249688, 336134793648, 1765105097640, 9267826715912, 48663053519336, 255518422362912, 1341650195416352

Offset

1,1

Comments

Column 2 of A206118.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 19*a(n-2) + 6*a(n-3) - 90*a(n-4) + 19*a(n-5) + 45*a(n-6) for n>8.

Empirical g.f.: 4*x*(285 + 737*x - 2373*x^2 - 9967*x^3 + 1778*x^4 + 16011*x^5 + 1206*x^6 - 3645*x^7) / ((1 - x)*(1 - x - x^2)*(1 - 19*x^2 - 45*x^3)). - Colin Barker, Jun 13 2018

Example

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

Crossrefs

Cf. A206118.

Sequence in context: A357496 A113708 A353066 * A232133 A261572 A252476

Adjacent sequences: A206109 A206110 A206111 * A206113 A206114 A206115

Keyword

nonn

Author

R. H. Hardin, Feb 03 2012

Status

approved