

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
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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

Table of n, a(n) for n=1..26.
R. E. Odeh and E. J. Cockayne, Balancing weights on the integer line, J. Combin. Theory, 7 (1969), 130135.


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}] (* JeanFrançois 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

N. J. A. Sloane.


EXTENSIONS

More terms from Henry Bottomley, Aug 09 2002


STATUS

approved



