A233164 Number of n X 4 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).

11, 64, 1280, 28672, 720896, 19922944, 587202560, 17985175552, 562640715776, 17798344474624, 566248488304640, 18067175067615232, 577305177233555456, 18460254872591663104, 590511983140819435520, 18892924695992401395712

Offset

1,1

Links

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

Formula

Empirical: a(n) = 48*a(n-1) - 512*a(n-2) for n>3.

Conjectures from Colin Barker, Oct 09 2018: (Start)

G.f.: x*(11 - 464*x + 3840*x^2) / ((1 - 16*x)*(1 - 32*x)).

a(n) = 4^(2*n-3) * (2^n+12) for n>1.

(End)

Example

Some solutions for n=4:
..0..1..2..1....0..1..7..1....0..1..0..1....0..1..0..1....0..1..0..2
..5..3..0..4....2..3..2..4....2..3..2..4....2..3..5..4....3..2..4..1
..0..6..5..6....1..0..6..0....0..6..7..6....0..1..0..1....0..6..0..2
..5..3..7..4....5..4..2..4....5..3..2..3....5..4..5..4....3..5..3..6

Crossrefs

Column 4 of A233168.

Sequence in context: A285361 A237358 A250604 * A215445 A184055 A332750

Adjacent sequences: A233161 A233162 A233163 * A233165 A233166 A233167

Keyword

nonn

Author

R. H. Hardin, Dec 05 2013

Status

approved