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Search: id:A002838
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| A002838 |
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Balancing weights on the integer line.
(Formerly M1419 N0556)
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+0
4
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| 1, 2, 5, 12, 32, 94, 289, 910, 2934, 9686, 32540, 110780, 381676, 1328980, 4669367, 16535154, 58965214, 211591218, 763535450, 2769176514, 10089240974, 36912710568, 135565151486, 499619269774, 1847267563742, 6850369296298
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Also number of partitions of n(n+1)/2 into up to n parts each no greater than n+1, partitions of n(n+3)/2 into exactly n parts each no greater than n+2 and partitions of n(n+1) into exactly n distinct parts each no greater than 2n+1, thus providing balancing solutions for n weights in distinct integer positions on [ -n,n] with a pivot at 0. - Henry Bottomley (se16(AT)btinternet.com), Aug 09 2002
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REFERENCES
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R. E. Odeh and E. J. Cockayne, Balancing weights on the integer line, J. Combin. Theory, 7 (1969), 130-135.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
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a(n) =A047997(n, n) =A067059(n, n+1). a(n) tends towards (sqrt(12)/pi)*4^n/n^2 and something like (sqrt(12)/pi)*4^n/(n^2+1.85*n+0.8) seems to give an even closer approximation. - Henry Bottomley (se16(AT)btinternet.com), Aug 09 2002
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CROSSREFS
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Cf. A047997.
Sequence in context: A148281 A148282 A148283 this_sequence A076822 A143657 A014326
Adjacent sequences: A002835 A002836 A002837 this_sequence A002839 A002840 A002841
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Henry Bottomley (se16(AT)btinternet.com), Aug 09 2002
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