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).

1, 1, 3, 11, 48, 236, 1248, 6896, 39168, 226496, 1325568, 7821056, 46399488, 276294656, 1649369088, 9862639616, 59041579008, 353712521216, 2120127479808, 12712174616576, 76238687305728, 457294683570176, 2743218342985728

Offset

1,3

Comments

Column 1 of A233168.

Links

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

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

Adjacent sequences: A233159 A233160 A233161 * A233163 A233164 A233165

Keyword

nonn

Author

R. H. Hardin, Dec 05 2013

Status

approved