%I A002838 M1419 N0556
%S A002838 1,2,5,12,32,94,289,910,2934,9686,32540,110780,381676,1328980,4669367,
%T A002838 16535154,58965214,211591218,763535450,2769176514,10089240974,
%U A002838 36912710568,135565151486,499619269774,1847267563742,6850369296298
%N A002838 Balancing weights on the integer line.
%C A002838 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
%D A002838 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002838 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002838 R. E. Odeh and E. J. Cockayne, Balancing weights on the integer line, 
               J. Combin. Theory, 7 (1969), 130-135.
%F A002838 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
%Y A002838 Cf. A047997.
%Y A002838 Sequence in context: A148281 A148282 A148283 this_sequence A076822 A143657 
               A014326
%Y A002838 Adjacent sequences: A002835 A002836 A002837 this_sequence A002839 A002840 
               A002841
%K A002838 nonn,easy,nice
%O A002838 1,2
%A A002838 N. J. A. Sloane (njas(AT)research.att.com).
%E A002838 More terms from Henry Bottomley (se16(AT)btinternet.com), Aug 09 2002