cp's OEIS Frontend

A138237 Number of unlabeled graphs with at least one cycle in which every connected component has at most one cycle.

%I A138237 #3 Mar 31 2012 14:43:49
%S A138237 1,3,9,26,71,197,543,1507,4186,11722,32883,92724,262179,743792,
%T A138237 2115019,6028779,17217093,49258009,141142096,404997704,1163569094,
%U A138237 3346830818,9636723582,27774427243,80121104084,231317022483,668346261557
%N A138237 Number of unlabeled graphs with at least one cycle in which every connected component has at most one cycle.
%H A138237 Wikipedia, <a href="http://en.wikipedia.org/wiki/Pseudoforest">Pseudoforest</a>.
%F A138237 a(n) = A134964(n) - A005195(n).
%e A138237 a(9)=543 since we have several cases, with one unicyclic graph, or two, or three. Namely,
%e A138237 -One triangle and a forest of order 6, or 20 graphs.
%e A138237 -One unicyclic graph with 4 nodes and a forest of order 5, or 20 graphs.
%e A138237 -One unicyclic graph with 5 nodes and a forest of order 4, or 30 graphs.
%e A138237 -One unicyclic graph with 6 nodes and a forest of order 3, or 39 graphs.
%e A138237 -One unicyclic graph of 7 nodes and a forest of order 2, or 66 graphs.
%e A138237 -One unicyclic graph of 8 nodes and an isolated vertex, or 89 graphs.
%e A138237 -One unicyclic graph of 9 nodes, or 240 graphs.
%e A138237 -Two triangles and a forest of order 3, or 3 graphs.
%e A138237 -One triangle plus one unicyclic graph of 4 nodes plus a forest of order 2, or 4 graphs.
%e A138237 -One triangle plus one unicyclic graph of 5 nodes plus an isolated vertex, or 5 graphs.
%e A138237 -One triangle plus one unicyclic graph of 6 nodes, or 13 graphs.
%e A138237 -Two unicyclic graphs of 4 nodes and an isolated vertex, or C(2+2-1,2)=3 graphs.
%e A138237 -One unicyclic graph of 5 nodes and another of 4 nodes, or 10 graphs.
%e A138237 -Three triangles, or 1 graph.
%e A138237 Total = 543.
%Y A138237 Cf. A001429, A005195, A140145.
%K A138237 nonn
%O A138237 3,2
%A A138237 _Washington Bomfim_, May 17 2008