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A233162 Number of n X 1 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 (unlabeled 8-colorings 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
J. R. Britnell and M. Wildon, Bell numbers, partition moves and the eigenvalues of the random-to-top shuffle in types A, B and D, arXiv 1507.04803 [math.CO], 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(n-1) -44*a(n-2) +48*a(n-3) 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^(n-6)*(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: A316703 A362741 A192399 * A345341 A186185 A367874
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 05 2013
STATUS
approved

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Last modified July 12 12:19 EDT 2024. Contains 374247 sequences. (Running on oeis4.)