A320499 Number of connected self-dual signed graphs with n nodes.

1, 1, 0, 1, 3, 14, 62, 572, 7409, 163284, 5736443, 342169618, 33534945769, 5442700283638, 1484664946343496, 664513607618098252, 508538464299389501337, 635542752091150346032474, 1374528064543283977151585962, 4842758246111267151697826493193

Offset

0,5

Links

Table of n, a(n) for n=0..19.

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. 273, fourth table.

Andrew Howroyd, PARI Program

Formula

a(2*n-1) = b(2*n-1), a(2*n) = b(2*n) - (A053465(n) - a(n))/2 where b is the Inverse Euler transform of A004104. - Andrew Howroyd, Jan 27 2020

Prog

(PARI) \\ See link for program.
A320499seq(20) \\ Andrew Howroyd, Jan 27 2020

Crossrefs

Cf. A004102 (signed graphs), A004104 (self-dual), A053465 (connected signed graphs).

Sequence in context: A237608 A100295 A291025 * A091701 A242637 A151237

Adjacent sequences: A320496 A320497 A320498 * A320500 A320501 A320502

Keyword

nonn

Author

N. J. A. Sloane, Oct 26 2018

Extensions

Dead sequence restored by Andrew Howroyd, Jan 26 2020

a(0)=1 prepended and terms a(13) and beyond from Andrew Howroyd, Jan 26 2020

Status

approved