A339847 The number of labeled 6-regular graphs on n nodes.

1, 0, 0, 0, 0, 0, 0, 1, 105, 30016, 11180820, 5188453830, 2977635137862, 2099132870973600, 1803595358964773088, 1872726690127181663775, 2329676580698022197516875, 3443086402825299720403673760, 5997229769947050271535917422040, 12218901113752712984458458475480428

Offset

0,9

Links

Marni Mishna, Table of n, a(n) for n = 0..195 (terms 0..36 from Andrew Howroyd, terms 37..40 from Atabey Kaygun)

Frédéric Chyzak and Marni Mishna Differential equations satisfied by generating functions of 5-, 6-, and 7-regular labelled graphs: a reduction-based approach, arXiv:2406.04753 [math.CO], 2024.

Atabey Kaygun, Counting Graphs with a Prescribed Degree Sequence.

Atabey Kaygun, Common LISP program that generates the sequence.

Atabey Kaygun, Enumerating Labeled Graphs that Realize a Fixed Degree Sequence, arXiv:2101.02299 [math.CO], 2021.

Marni Mishna, Maple code to generate terms.

Prog

(PARI) \\ Needs GraphsByDegreeSeq from links in A295193.
a(n)={my(M=GraphsByDegreeSeq(n, 6, (p, r)->6-valuation(p, x) <= r)); if(n>=7, vecsum(M[, 2]), n==0)} \\ Andrew Howroyd, Dec 26 2020

Crossrefs

Column k=6 of A059441.

Cf. A165627 (unlabeled case), A295193.

Sequence in context: A111647 A368513 A295463 * A145621 A167779 A275461

Adjacent sequences: A339844 A339845 A339846 * A339848 A339849 A339850

Keyword

nonn

Author

Atabey Kaygun, Dec 21 2020

Extensions

Terms a(14) and beyond from Andrew Howroyd, Dec 26 2020

Status

approved