A320993 Number of connected self-dual marked graphs on 2n nodes.

1, 1, 6, 81, 2796, 285205, 96322648, 112087066485, 458071927263177, 6665704296474517580, 349377209492189224235030, 66602723163954143548104716149, 46557323273646194397454383970079368, 120168498151800396724425771086539073209571, 1152049915423012273792614840558950392103437052846

Offset: 0

Author

N. J. A. Sloane, Oct 26 2018

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..50
• Edward A. Bender and E. Rodney Canfield, Enumeration of connected invariant graphs, Journal of Combinatorial Theory, Series B 34.3 (1983): 268-278. See p. 274.
• Andrew Howroyd, PARI Program

Crossrefs

Cf. A000666 (not necessarily connected marked graphs), A000595 (self dual on 2n nodes), A054921 (connected marked graphs).

Programs

PARI

\\ See link for program.
A320993seq(15) \\ Andrew Howroyd, Jan 27 2020

Formula

a(2*n-1) = b(2*n-1) - A054921(2*n-1)/2, a(2*n) = b(2*n) - (A054921(2*n)-a(n))/2 where b is the Inverse Euler transform of A000595. - Andrew Howroyd, Jan 27 2020

Extensions

a(0)=1 prepended and terms a(7) and beyond from Andrew Howroyd, Jan 26 2020