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 A306003 Number of simple graphs on n nodes where each component has at least one cycle. 2
 0, 0, 1, 4, 18, 107, 846, 11122, 261212, 11717906, 1006716728, 164060156360, 50335920919080, 29003488522658695, 31397381311096116107, 63969560164236980493127, 245871831711291931225960094, 1787331725280413408599670721723, 24636021429463963332562215579906526 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 16 13:05 EDT 2024. Contains 373429 sequences. (Running on oeis4.)