A007695 Cardinalities of Sperner families on 1,...,n. (Formerly M2466)

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

Offset

0,1

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

Table of n, a(n) for n=0..16.

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.

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<kap[ r, x ], d -= c[ r-1, j ]; j++ ]; c[ r, x ]=d; s += d; ] ]; s ]

Crossrefs

This is the limiting form of A011828-A011833.

Cf. A001405.

Sequence in context: A011831 A011832 A011833 * A296261 A133662 A204518

Adjacent sequences: A007692 A007693 A007694 * A007696 A007697 A007698

Keyword

nonn,nice

Author

N. J. A. Sloane, Don Knuth

Extensions

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

Status

approved