OFFSET
1,2
COMMENTS
From Gus Wiseman, Mar 01 2019: (Start)
Also the number of stable partitions of the n-ladder graph. A stable partition of a graph is a set partition of the vertices where no edge has both ends in the same block. The n-ladder has 2n vertices and looks like:
o-o-o- -o
| | | ... |
o-o-o- -o
(End)
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..61
FORMULA
It appears that the sequence terms are given by the Dobinski-type formula a(n+1) = (1/e) * Sum_{k>=0} (1+k+k^2)^n/k!. - Peter Bala, Mar 12 2012
Apply x^n -> B(n) to the polynomial chi(n) = x (x - 1) (x^2 - 3 x + 3)^(n - 1), where B = A000110. - Gus Wiseman, Mar 01 2019
EXAMPLE
Some solutions for n=5:
0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
1 0 1 0 1 2 1 2 1 0 1 0 1 2 1 0 1 0 1 0
0 1 0 1 0 1 0 1 2 1 0 1 0 1 0 2 2 1 0 1
1 2 1 0 1 0 1 3 3 0 2 0 3 2 2 1 1 0 1 2
0 1 0 1 2 1 2 4 1 2 0 1 0 1 0 2 0 1 2 0
MATHEMATICA
Table[Expand[x*(x-1)*(x^2-3*x+3)^(n-1)]/.x^k_.->BellB[k], {n, 20}] (* Gus Wiseman, Mar 01 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, Feb 21 2012
STATUS
approved