A138237 - OEIS

%I #3 Mar 31 2012 14:43:49

%S 1,3,9,26,71,197,543,1507,4186,11722,32883,92724,262179,743792,

%T 2115019,6028779,17217093,49258009,141142096,404997704,1163569094,

%U 3346830818,9636723582,27774427243,80121104084,231317022483,668346261557

%N Number of unlabeled graphs with at least one cycle in which every connected component has at most one cycle.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Pseudoforest">Pseudoforest</a>.

%F a(n) = A134964(n) - A005195(n).

%e a(9)=543 since we have several cases, with one unicyclic graph, or two, or three. Namely,

%e -One triangle and a forest of order 6, or 20 graphs.

%e -One unicyclic graph with 4 nodes and a forest of order 5, or 20 graphs.

%e -One unicyclic graph with 5 nodes and a forest of order 4, or 30 graphs.

%e -One unicyclic graph with 6 nodes and a forest of order 3, or 39 graphs.

%e -One unicyclic graph of 7 nodes and a forest of order 2, or 66 graphs.

%e -One unicyclic graph of 8 nodes and an isolated vertex, or 89 graphs.

%e -One unicyclic graph of 9 nodes, or 240 graphs.

%e -Two triangles and a forest of order 3, or 3 graphs.

%e -One triangle plus one unicyclic graph of 4 nodes plus a forest of order 2, or 4 graphs.

%e -One triangle plus one unicyclic graph of 5 nodes plus an isolated vertex, or 5 graphs.

%e -One triangle plus one unicyclic graph of 6 nodes, or 13 graphs.

%e -Two unicyclic graphs of 4 nodes and an isolated vertex, or C(2+2-1,2)=3 graphs.

%e -One unicyclic graph of 5 nodes and another of 4 nodes, or 10 graphs.

%e -Three triangles, or 1 graph.

%e Total = 543.

%Y Cf. A001429, A005195, A140145.

%K nonn

%O 3,2

%A _Washington Bomfim_, May 17 2008