

A233164


Number of n X 4 0..7 arrays with no element x(i,j) adjacent to itself or value 7x(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 8colorings with no clashing color pairs).


1



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

1,1


LINKS

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


FORMULA

Empirical: a(n) = 48*a(n1)  512*a(n2) 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*n3) * (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



