

A006787


Number of nnode graphs with no cycles of length less than 5.
(Formerly M0792)


9



1, 2, 3, 6, 11, 23, 48, 114, 293, 869, 2963, 12066, 58933, 347498, 2455693, 20592932, 202724920, 2322206466, 30743624324, 468026657815, 8161170076257
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OFFSET

1,2


COMMENTS

Includes graphs with no cycles at all as well as graphs with girth greater than 5.


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Table of n, a(n) for n=1..21.
CombOS  Combinatorial Object Server, Generate graphs
Brendan McKay, Emails to N. J. A. Sloane, 1991
Brendan D. McKay, Isomorphfree exhaustive generation, Table 2.
Brendan D. McKay, IsomorphFree Exhaustive Generation, J. Algorithms, vol. 26 iss. 2 (1998), 306324.


FORMULA

a(n) = A000088(n)  A128236(n)  A128237(n).  Andrew Howroyd, May 06 2021


CROSSREFS

Cf. A000066, A000088, A054760, A159847, A126757 (connected, inv. Eul. Transf.), A128236, A128237, A300705.
Sequence in context: A123465 A000055 A217312 * A176425 A000992 A036648
Adjacent sequences: A006784 A006785 A006786 * A006788 A006789 A006790


KEYWORD

nonn,more


AUTHOR

N. J. A. Sloane


EXTENSIONS

Definition corrected by Brendan McKay, Apr 27 2007
a(18)a(19) (from the McKay reference) added by R. J. Mathar, Jun 17 2008
a(20)a(21) from Brendan McKay, Mar 11 2018


STATUS

approved



