A006787 Number of n-node graphs with no cycles of length less than 5. (Formerly M0792)

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

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, Isomorph-free exhaustive generation, Table 2.

Brendan D. McKay, Isomorph-Free Exhaustive Generation, J. Algorithms, vol. 26 iss. 2 (1998), 306-324.

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