A306003 Number of simple graphs on n nodes where each component has at least one cycle.

0, 0, 1, 4, 18, 107, 846, 11122, 261212, 11717906, 1006716728, 164060156360, 50335920919080, 29003488522658695, 31397381311096116107, 63969560164236980493127, 245871831711291931225960094, 1787331725280413408599670721723, 24636021429463963332562215579906526

Offset

1,4

Comments

Euler transform of A241841. Here the graphs are simple (no loops, no multi-edges) but not necessarily connected.

Links

Georg Fischer, Table of n, a(n) for n = 1..40

Example

a(7) = 846 counts A241841(7) = 842 graphs with one component plus 4 graphs with two components (the two components being the connected graph on 3 nodes and any of the 4 graphs on 4 nodes).
a(8) = 11122 counts A241841(8) = 11094 graphs with one component and 28 graphs with two components.
a(9) = 261212 counts A241841(9) = 261033 graphs with one component, 178 graphs with two components, and 1 graph with 3 components.

Crossrefs

Cf. A241841 (connected variant), A286743 (at least one component has one cycle).

Sequence in context: A009597 A241841 A241842 * A214840 A060223 A144085

Adjacent sequences: A306000 A306001 A306002 * A306004 A306005 A306006

Keyword

nonn

Author

R. J. Mathar, Jun 16 2018

Extensions

a(19) corrected by Georg Fischer, Dec 20 2022

Status

approved