|
| |
|
|
A002838
|
|
Balancing weights on the integer line.
(Formerly M1419 N0556)
|
|
4
| |
|
|
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; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| 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
|
|
|
REFERENCES
| 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).
|
|
|
FORMULA
| 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
|
|
|
CROSSREFS
| Cf. A047997.
Sequence in context: A148282 A148283 * A076822 A143657 A014326 A148284
Adjacent sequences: A002835 A002836 A002837 * A002839 A002840 A002841
|
|
|
KEYWORD
| nonn,easy,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from Henry Bottomley (se16(AT)btinternet.com), Aug 09 2002
|
| |
|
|
