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A304071 Number of simple connected graphs with n nodes rooted at one non-edge. 2
0, 0, 1, 6, 42, 402, 5381, 112776, 3935471, 240684836, 26449057257, 5289513580458 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..12.

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.

CROSSREFS

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

Sequence in context: A074107 A187121 A225497 * A052608 A245248 A197712

Adjacent sequences:  A304068 A304069 A304070 * A304072 A304073 A304074

KEYWORD

nonn,more

AUTHOR

Brendan McKay, May 05 2018

STATUS

approved

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Last modified March 24 19:48 EDT 2019. Contains 321448 sequences. (Running on oeis4.)