A322555 Number of labeled simple graphs on n vertices where all non-isolated vertices have the same degree.

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.

Links

Table of n, a(n) for n=0..18.

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}]

Crossrefs

Cf. A000569, A005176, A038041, A059441, A295193, A306017, A306019, A319169, A320458.

Sequence in context: A363061 A288910 A249062 * A118814 A345878 A014271

Adjacent sequences: A322552 A322553 A322554 * A322556 A322557 A322558

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