A126133 Number of edge-rooted unlabeled graphs with n edges.

1, 2, 7, 21, 66, 210, 699, 2387, 8492, 31329, 120034, 477028, 1965016, 8377888, 36923184, 167972182, 787688821, 3802526173, 18873118341, 96195592212, 502953711022, 2694740822749, 14781176429303, 82931707378322

Offset

1,2

References

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973.

Links

Max Alekseyev, Table of n, a(n) for n = 1..40

Formula

G.f.: f(x)*x/(1 + x) where f(x) is the g.f. of A339064. - Andrew Howroyd, Nov 22 2020

Example

a(3)=7: the triangular graph with one edge rooted. The disconnected graph of the connected linear graph with 3 nodes aside the connected graph with 2 nodes, 2 choices for the root. The three disconnected graphs with 3 graphs on 2 nodes, one of the three with the root. The connected star graph with one edge rooted. The connected linear graph with four nodes, 2 choices for the root. - R. J. Mathar, May 03 2018

Prog

(PARI) \\ See A339063 for G.
seq(n)={my(A=O(x*x^n)); Vec((G(2*n, x+A, [1, 1]) + G(2*n, x+A, [2]))/(2*(1+x)))} \\ Andrew Howroyd, Nov 21 2020

Crossrefs

Cf. A000664, A126122, A303832 (connected), A339063, A339064.

Sequence in context: A218836 A331722 A052911 * A344500 A186240 A274203

Adjacent sequences: A126130 A126131 A126132 * A126134 A126135 A126136

Keyword

nonn

Author

Vladeta Jovovic, Mar 07 2007

Extensions

Terms a(10) onward from Max Alekseyev, May 03 2018

Status

approved