A007695 Cardinalities of Sperner families on 1,...,n.

2, 3, 5, 10, 26, 96, 553, 5461, 100709, 3718354, 289725509, 49513793526, 19089032278261, 16951604697397302, 35231087224279091310, 173550485517380958360611, 2047581288200721764035942914

Offset: 0

Author

N. J. A. Sloane, Don Knuth

Keywords

• nonn
• nice

Comments

Also number of f-vectors for simplicial complexes on at most n vertices.

References

• S. Johnson, Upper bounds for constant weight error correcting codes, Discrete Math., 3 (1972), 109-124.
• D. E. Knuth, The Art of Computer Programming, vol. 4A, Combinatorial Algorithms, Section 7.2.1.3 (p. 743).
• D. E. Knuth, Art of Computer Programming, Vol. 4, Section 7.3, to appear.
• S. Linusson, The number of M-sequences and f-vectors, Combinatorica, 19 (1999), 255-266.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• D. Knuth, Email to N. J. A. Sloane, Aug. 1994.
• Tamon Stephen and Timothy Yusun, Counting inequivalent monotone Boolean functions, arXiv preprint arXiv:1209.4623 [cs.DS], 2012.

Crossrefs

This is the limiting form of A011828-A011833.

Cf. A001405.

Programs

Mathematica

c[ 0, 0 ]=1; c[ 0, 1 ]=1; kap[ 0, 0 ]=0; f[ n_ ] := Block[ {s=2, r, d, k, j}, For[ r=1, r<=n, r++, d=s; k=r; j=0; s=0;
For[ x=0, x<=Binomial[ n, r ], x++, If[ x>=Binomial[ k, r ], k++, 0 ]; kap[ r, x ]=If[ x==0, 0, Binomial[ k-1, r-1 ]+kap[ r-1, x-Binomial[ k-1, r ] ] ];
While[ j
				

Extensions

Entry revised by N. J. A. Sloane, Sep 03 2011