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Revision History for A306003

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A306003

Number of simple graphs on n nodes where each component has at least one cycle.
(history; published version)

#5 by R. J. Mathar at Sat Jun 16 13:52:34 EDT 2018

STATUS

editing

proposed

#4 by R. J. Mathar at Sat Jun 16 13:52:30 EDT 2018

COMMENTS

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

#3 by R. J. Mathar at Sat Jun 16 13:45:15 EDT 2018

NAME

allocated for R. J. Mathar

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

DATA

0, 0, 1, 4, 18, 107, 846, 11122, 261212, 11717906, 1006716728, 164060156360, 50335920919080, 29003488522658695, 31397381311096116107, 63969560164236980493127, 245871831711291931225960094, 1787331725280413408599670721723, 2463602142946396333256221557990652

OFFSET

1,4

COMMENTS

Euler transform of A241841.

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), A306004.

KEYWORD

allocated

nonn

AUTHOR

R. J. Mathar, Jun 16 2018

STATUS

approved

editing

#2 by R. J. Mathar at Sat Jun 16 13:37:22 EDT 2018

KEYWORD

allocating

allocated

#1 by R. J. Mathar at Sat Jun 16 13:37:22 EDT 2018

NAME

allocated for R. J. Mathar

KEYWORD

allocating

STATUS

approved