A327373 BII-numbers of complete simple graphs.

0, 1, 4, 52, 2868, 9112372, 141334497921844, 39614688284139543691484924724, 3138550868424102398255194438067307501961665532948002835252, 19701003098197239607207513568280927372312554341759233318802451615112823176074440555010583132712036457851366790597428

Offset: 0

Author

Gus Wiseman, Sep 04 2019

Keywords

• nonn

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.

Crossrefs

BII-numbers of uniform set-systems are A326783.

BII-numbers of maximal uniform set-systems are A327080.

BII-numbers of maximal uniform normal set-systems are A327081.

Cf. A000120, A006125, A018900, A029931, A048793, A070939, A326031, A326784, A326785, A327041.

Programs

Mathematica

Table[If[n==1,1,Total[2^(Total[2^#]/2&/@Subsets[Range[n],{2}])]/2],{n,0,10}]