A304071 Number of simple connected graphs with n nodes rooted at one non-edge.

0, 0, 1, 6, 42, 402, 5381, 112776, 3935471, 240684836, 26449057257, 5289513580458, 1939502108505917, 1311274498490104492, 1642800188822966309834, 3831285832174735713684706, 16703340559932677463553709189, 136661710199022168890320488632600, 2105815888079982128884579271408161673, 61310553163194788144046000967760340771668

Offset

1,4

Links

Jean-François Alcover, Table of n, a(n) for n = 1..40

Formula

a(n) + A303830(n) = A303831(n).

Example

a(3)=1: the non-edge joins the two leaves. a(4)=6: quadrangle: the non-edge is a diagonal; triangle with protruding edge: the non-edge joins the leaf with a node of degree 2; quadrangle with diagonal: the non-edge is the other diagonal; tetrahedron: no contribution; linear chain: the non-edge either joins the two leaves or a leaf with a node at distance 2; star graph: the non-edge joins two leaves.

Mathematica

A303830 = Import["https://oeis.org/A303830/b303830.txt", "Table"][[All, 2]];
A303831 = Import["https://oeis.org/A303831/b303831.txt", "Table"][[All, 2]];
a[n_] := A303831[[n]] - A303830[[n]];
a /@ Range[1, 40] (* Jean-François Alcover, Sep 21 2019 *)

Crossrefs

Cf. A001349 (not rooted), A126122 (not necessarily connected)

Sequence in context: A187121 A225497 A336950 * A052608 A245248 A197712

Adjacent sequences: A304068 A304069 A304070 * A304072 A304073 A304074

Keyword

nonn

Author

Brendan McKay, May 05 2018

Status

approved