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A140636
Number of connected graphs on n unlabeled nodes that contain at least two cycles.
9
0, 0, 0, 2, 13, 93, 809, 11005, 260793, 11715808, 1006698524, 164059824899, 50335907853919, 29003487462805642, 31397381142761123838, 63969560113225175845492, 245871831682084026518599099, 1787331725248899088890197955308, 24636021429399867655322650752269938
OFFSET
1,4
COMMENTS
Original name: number of unlabeled complex components with n nodes.
We can find in "The Birth of the Giant Component", p. 2, see the first link:
"As each of the random graphs evolved, the story went, never once was there more than a single 'complex' component; i.e. there never were two or more components present simultaneously that were neither trees nor unicyclic."
So a complex component is a connected graph that is neither a tree nor an unicyclic graph.
LINKS
Svante Janson, Donald E. Knuth, Tomasz Luczak and Boris Pittel, The Birth of the Giant Component, [DOI], Rand. Struct. Alg. 4 (3) (1993) 233-358
FORMULA
a(n) = A001349(n) - A005703(n).
a(n) = A001349(n) - A000055(n) - A001429(n).
EXAMPLE
a(4) = 2. See the two complex components with 4 nodes in the Sloane illustration.
CROSSREFS
The labeled version is A140638.
Sequence in context: A199489 A300764 A209470 * A369413 A282724 A104255
KEYWORD
nonn
AUTHOR
Washington Bomfim, May 20 2008
EXTENSIONS
Name changed by Andrew Howroyd, Jan 16 2022
STATUS
approved