This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A002838 Balancing weights on the integer line. (Formerly M1419 N0556) 8
 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; text; 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, Aug 09 2002 Is this a shifted version of A076822 ? -Vladimir Reshetnikov, Oct 06 2016 REFERENCES 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). LINKS R. E. Odeh and E. J. Cockayne, Balancing weights on the integer line, J. Combin. Theory, 7 (1969), 130-135. 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, Aug 09 2002 MATHEMATICA (* This program is not convenient for large values of n *) a[n_] := Length[ IntegerPartitions[n*(n+1)/2, n, Range[n+1]]]; Table[ Print[{n, an = a[n]}]; an, {n, 1, 16}] (* Jean-François Alcover, Jan 02 2013 *) CROSSREFS Cf. A047997, A076822, A188181 (columns 1, 2). Sequence in context: A148283 A218781 * A076822 A143657 A014326 A148284 Adjacent sequences:  A002835 A002836 A002837 * A002839 A002840 A002841 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS More terms from Henry Bottomley, Aug 09 2002 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 12 07:00 EST 2018. Contains 318051 sequences. (Running on oeis4.)