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
Keywords
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.
Programs
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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
Extensions
Terms a(14) and beyond from Andrew Howroyd, Dec 26 2020