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

0,3

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

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

Prog

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

Crossrefs

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

Sequence in context: A076282 A121790 A279203 * A032491 A135624 A222197

Adjacent sequences: A320990 A320991 A320992 * A320994 A320995 A320996

Keyword

nonn

Author

N. J. A. Sloane, Oct 26 2018

Extensions

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

Status

approved