

A233162


Number of n X 1 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).


7



1, 1, 3, 11, 48, 236, 1248, 6896, 39168, 226496, 1325568, 7821056, 46399488, 276294656, 1649369088, 9862639616, 59041579008, 353712521216, 2120127479808, 12712174616576, 76238687305728, 457294683570176, 2743218342985728
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

Column 1 of A233168.


LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210
J. R. Britnell, M. Wildon, Bell numbers, partition moves and the eigenvalues of the randomtotop shuffle in types A, B and D, arXiv 1507.04803, 2015. [I assume the connection mentioned in this paper will mean that the "Empirical" comment in the recurrence could be removed.  N. J. A. Sloane, Feb 27 2016]


FORMULA

Empirical: a(n) = 12*a(n1) 44*a(n2) +48*a(n3) for n>4.
Conjectures from Colin Barker, Feb 18 2018: (Start)
G.f.: x*(1  11*x + 35*x^2  29*x^3) / ((1  2*x)*(1  4*x)*(1  6*x)).
a(n) = (2^(n6)*(90 + 9*2^n + 2*3^n)) / 9 for n>1.
(End)


EXAMPLE

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


CROSSREFS

Cf. A233168.
Sequence in context: A121139 A316703 A192399 * A186185 A317170 A127087
Adjacent sequences: A233159 A233160 A233161 * A233163 A233164 A233165


KEYWORD

nonn


AUTHOR

R. H. Hardin, Dec 05 2013


STATUS

approved



