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Search: id:A007695
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| A007695 |
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Cardinalities of Sperner families on 1,...,n.
(Formerly M2466)
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+0
1
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| 3, 5, 10, 26, 96, 553, 5461, 100709, 3718354, 289725509, 49513793526, 19089032278261, 16951604697397302, 35231087224279091310, 173550485517380958360611, 2047581288200721764035942914
(list; graph; listen)
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OFFSET
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1,1
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
S. Johnson, Upper bounds for constant weight error correcting codes, Discrete Math., 3 (1972), 109-124.
D. E. Knuth, Art of Computer Programming, Vol. 4, Section 7.3.
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MATHEMATICA
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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
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Cf. A001405.
Sequence in context: A080522 A132332 A002039 this_sequence A011969 A003187 A100885
Adjacent sequences: A007692 A007693 A007694 this_sequence A007696 A007697 A007698
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), D. E. Knuth
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