

A327106


BIInumbers of setsystems with maximum degree 2.


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
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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 setsystem with BIInumber n to be obtained by taking the binary indices of each binary index of n. Every setsystem (finite set of finite nonempty sets) has a different BIInumber. 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 BIInumber of {{2},{1,3}} is 18. Elements of a setsystem are sometimes called edges.
In a setsystem, 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 setsystems with maximum degree 2 together with their BIInumbers 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



