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A007695
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Cardinalities of Sperner families on 1,...,n.
(Formerly M2466)
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3
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2, 3, 5, 10, 26, 96, 553, 5461, 100709, 3718354, 289725509, 49513793526, 19089032278261, 16951604697397302, 35231087224279091310, 173550485517380958360611, 2047581288200721764035942914
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Also number of f-vectors for simplicial complexes on at most n vertices.
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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).
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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 ]
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CROSSREFS
| This is the limiting form of A011828-A011833.
Cf. A001405.
Sequence in context: A011831 A011832 A011833 * A133662 A204518 A088938
Adjacent sequences: A007692 A007693 A007694 * A007696 A007697 A007698
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), D. E. Knuth
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EXTENSIONS
| Entry revised by N. J. A. Sloane, Sep 03 2011
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