A126757 Number of n-node connected graphs with no cycles of length less than 5.

1, 1, 1, 2, 4, 8, 18, 47, 137, 464, 1793, 8167, 43645, 275480, 2045279, 17772647, 179593823, 2098423758, 28215583324, 434936005284, 7662164738118

Offset: 1

Author

N. J. A. Sloane, Feb 18 2007

Keywords

• nonn
• more

Links

• Keith M. Briggs, Combinatorial Graph Theory
• CombOS - Combinatorial Object Server, Generate graphs

Crossrefs

Cf. A006787, A140440.

Programs

Mathematica

A006787 = Cases[Import["https://oeis.org/A006787/b006787.txt", "Table"], {, }][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
EulerInvTransform[A006787] (* Jean-François Alcover, May 13 2019, updated Mar 17 2020 *)

Formula

This is the inverse Euler transform of A006787. - Conjectured by Vladeta Jovovic, Jun 16 2008, proved by Max Alekseyev and Brendan McKay, Jun 17 2008

Extensions

Definition corrected by Max Alekseyev and Brendan McKay, Jun 17 2008

a(20)-a(21) using Brendan McKay's extension to A006787 by Alois P. Heinz, Mar 11 2018