A233123 Number of n X 2 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

1, 8, 80, 896, 10496, 124928, 1495040, 17924096, 215023616, 2580021248, 30959206400, 371506282496, 4458058612736, 53496636243968, 641959366492160, 7703511324164096, 92442131595001856, 1109305561960153088

Offset

1,2

Comments

Column 2 of A233129.

Links

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

Formula

Empirical: a(n) = 16*a(n-1) - 48*a(n-2).

Conjectures from Colin Barker, Mar 19 2018: (Start)

G.f.: x*(1 - 8*x) / ((1 - 4*x)*(1 - 12*x)).

a(n) = 2^(2*n-3) * (3^n+3) / 3.

(End)

Example

Some solutions for n=5:
..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
..1..0....2..5....4..0....4..0....2..0....2..5....4..0....4..0....1..0....1..0
..0..1....0..4....5..2....2..1....0..2....4..3....2..1....5..2....5..2....5..1
..1..5....3..0....3..1....1..3....3..5....5..1....4..5....3..5....3..4....1..2
..0..4....0..2....0..2....2..4....0..4....1..3....0..1....0..2....1..0....0..1

Crossrefs

A233129.

Sequence in context: A102592 A345081 A320759 * A269796 A328128 A053175

Adjacent sequences: A233120 A233121 A233122 * A233124 A233125 A233126

Keyword

nonn

Author

R. H. Hardin, Dec 04 2013

Status

approved