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A322555
Number of labeled simple graphs on n vertices where all non-isolated vertices have the same degree.
1
1, 1, 2, 5, 18, 69, 390, 2703, 59474, 1548349, 168926258, 12165065351, 7074423247562, 2294426405580191, 4218009215702391954, 3810376434461484994317, 35102248193591661086921250, 156873334244228518638713087133, 4144940994226400702145709978234154
OFFSET
0,3
COMMENTS
Such graphs may be said to have regular support.
FORMULA
a(n) = 1 + Sum_{k=1..n} binomial(n, k)*(A295193(k) - 1). - Andrew Howroyd, Dec 17 2018
EXAMPLE
The a(4) = 18 edge sets:
{}
{{1,2}}
{{1,3}}
{{1,4}}
{{2,3}}
{{2,4}}
{{3,4}}
{{1,2},{3,4}}
{{1,3},{2,4}}
{{1,4},{2,3}}
{{1,2},{1,3},{2,3}}
{{1,2},{1,4},{2,4}}
{{1,3},{1,4},{3,4}}
{{2,3},{2,4},{3,4}}
{{1,2},{1,3},{2,4},{3,4}}
{{1,2},{1,4},{2,3},{3,4}}
{{1,3},{1,4},{2,3},{2,4}}
{{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}
MATHEMATICA
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], SameQ@@Length/@Split[Sort[Join@@#]]&]], {n, 6}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 15 2018
EXTENSIONS
a(8)-a(15) from Andrew Howroyd, Dec 17 2018
a(16)-a(18) from Andrew Howroyd, May 21 2020
STATUS
approved