OFFSET
1,3
COMMENTS
a(n) is the number of forests with n unlabeled nodes without trees of order 2. This follows from the fact that for n>=2 A005195(n-2) counts the forests of order n with one or more trees of order 2.
The unique forest of order 1 is an isolated vertex, so a(1)=1. For n>=2, a(n) - a(n-1) counts forests of order n with trees of order >=3.
EXAMPLE
a(5) = 7 since the only options are: 3 trees of order 5; 2 forests composed by trees of orders 4 and l; one forest with trees of orders [3 1 1]; and one forest with five isolated nodes.
CROSSREFS
KEYWORD
nonn
AUTHOR
Washington Bomfim, Sep 28 2008
STATUS
approved