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
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 05 2013
STATUS
approved