A327106 BII-numbers of set-systems with maximum degree 2.

5, 6, 7, 13, 14, 15, 17, 19, 20, 22, 24, 25, 26, 27, 28, 30, 34, 35, 36, 37, 40, 41, 42, 43, 44, 45, 48, 49, 50, 51, 52, 65, 66, 67, 68, 72, 73, 74, 75, 76, 80, 82, 96, 97, 133, 134, 135, 141, 142, 143, 145, 147, 148, 150, 152, 153, 154, 155, 156, 158, 162

Offset

1,1

Comments

A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793. We define the set-system with BII-number n to be obtained by taking the binary indices of each binary index of n. Every set-system (finite set of finite nonempty sets) has a different BII-number. For example, 18 has reversed binary expansion (0,1,0,0,1), and since the binary indices of 2 and 5 are {2} and {1,3} respectively, the BII-number of {{2},{1,3}} is 18. Elements of a set-system are sometimes called edges.

In a set-system, the degree of a vertex is the number of edges containing it.

Links

Table of n, a(n) for n=1..61.

Example

The sequence of all set-systems with maximum degree 2 together with their BII-numbers begins:
   5: {{1},{1,2}}
   6: {{2},{1,2}}
   7: {{1},{2},{1,2}}
  13: {{1},{1,2},{3}}
  14: {{2},{1,2},{3}}
  15: {{1},{2},{1,2},{3}}
  17: {{1},{1,3}}
  19: {{1},{2},{1,3}}
  20: {{1,2},{1,3}}
  22: {{2},{1,2},{1,3}}
  24: {{3},{1,3}}
  25: {{1},{3},{1,3}}
  26: {{2},{3},{1,3}}
  27: {{1},{2},{3},{1,3}}
  28: {{1,2},{3},{1,3}}
  30: {{2},{1,2},{3},{1,3}}
  34: {{2},{2,3}}
  35: {{1},{2},{2,3}}
  36: {{1,2},{2,3}}
  37: {{1},{1,2},{2,3}}

Mathematica

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[0, 100], If[#==0, 0, Max@@Length/@Split[Sort[Join@@bpe/@bpe[#]]]]==2&]

Crossrefs

Positions of 2's in A327104.

Graphs with maximum degree 2 are counted by A136284.

Cf. A000120, A048793, A058891, A070939, A326031, A326701, A326786, A327041, A327103.

Sequence in context: A011761 A106745 A165776 * A003273 A006991 A047574

Adjacent sequences: A327103 A327104 A327105 * A327107 A327108 A327109

Keyword

nonn

Author

Gus Wiseman, Aug 26 2019

Status

approved