

A326784


BIInumbers of regular setsystems.


10



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
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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 setsystem with BIInumber n to be obtained by taking the binary indices of each binary index of n. A setsystem is regular if all vertices appear the same number of times.


LINKS



EXAMPLE

The sequence of all regular setsystems together with their BIInumbers 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).


KEYWORD

nonn


AUTHOR



STATUS

approved



