A303831 Birooted graphs: number of unlabeled connected graphs with n nodes rooted at 2 indistinguishable roots.

0, 1, 3, 16, 98, 879, 11260, 230505, 7949596, 483572280, 53011686200, 10589943940654, 3880959679322754, 2623201177625659987, 3286005731275218388682, 7663042204550840483139108, 33407704152242477510352455230, 273327599183687887638526170380380

Offset: 1

Author

Brendan McKay, May 01 2018

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..40
• Jean-François Alcover, Mathematica program

Crossrefs

Cf. A303829 (not necessarily connected). 3rd column of A304311.

Cf. A000088 (not rooted), A126100 (connected single root), A053506 (2 roots adjacent).

Programs

Mathematica

(* See the links section. *)

Formula

G.f.: B(x)/G(x) - (C(x^2) + C(x)^2)/2 where B(x) is the g.f. of A303829, G(x) is the g.f. of A000088 and C(x) is the g.f. of A126100. - Andrew Howroyd, May 03 2018

a(n) = A303830(n) + A304071(n). - Brendan McKay, May 05 2018

Extensions

a(12)-a(18) from Andrew Howroyd, May 03 2018