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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 (unlabelled 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

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 random-to-top 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(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: 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

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Last modified June 15 21:17 EDT 2021. Contains 345050 sequences. (Running on oeis4.)