A326784 BII-numbers of regular set-systems.

0, 1, 2, 3, 4, 7, 8, 9, 10, 11, 12, 16, 18, 25, 30, 32, 33, 42, 45, 51, 52, 63, 64, 75, 76, 82, 94, 97, 109, 115, 116, 127, 128, 129, 130, 131, 132, 136, 137, 138, 139, 140, 144, 146, 160, 161, 192, 256, 258, 264, 266, 288, 385, 390, 408, 427, 428, 434, 458

Offset

1,3

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. A set-system is regular if all vertices appear the same number of times.

Links

Table of n, a(n) for n=1..59.

Example

The sequence of all regular set-systems together with their BII-numbers begins:
   0: {}
   1: {{1}}
   2: {{2}}
   3: {{1},{2}}
   4: {{1,2}}
   7: {{1},{2},{1,2}}
   8: {{3}}
   9: {{1},{3}}
  10: {{2},{3}}
  11: {{1},{2},{3}}
  12: {{1,2},{3}}
  16: {{1,3}}
  18: {{2},{1,3}}
  25: {{1},{3},{1,3}}
  30: {{2},{1,2},{3},{1,3}}
  32: {{2,3}}
  33: {{1},{2,3}}
  42: {{2},{3},{2,3}}
  45: {{1},{1,2},{3},{2,3}}
  51: {{1},{2},{1,3},{2,3}}

Mathematica

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

Crossrefs

Cf. A000120, A001511, A005176, A029931, A048793, A070939, A295193, A322554, A326031, A326701, A326783 (uniform), A326785 (uniform regular).

Sequence in context: A047549 A039074 A326966 * A047337 A039049 A037466

Adjacent sequences: A326781 A326782 A326783 * A326785 A326786 A326787

Keyword

nonn

Author

Gus Wiseman, Jul 25 2019

Status

approved