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why do recursive function calculations take so long in Mathematica?

• To: mathgroup at smc.vnet.net
• Subject: [mg43566] why do recursive function calculations take so long in Mathematica?
• From: g.feigin at verizon.net (G Feigin)
• Date: Sat, 20 Sep 2003 06:39:35 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

I defined the following simple recursive function:

dr[0,0] := 0; dr[n_,n_]:= 0;
dr[n_,0]:=1;dr[n_,k_]:=dr[n,k-1]+dr[n-1,k];

To evaluate dr[16,15] takes about 5 minutes on a Pentium class
machine, an absurdly long time.  Why? And what can I do to speed
things up?  By the way,
if I perform the recursion in an Excel spreadsheet on the same
machine, the calculation time is practically instantaneous.

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• Follow-Ups:
  • Re: why do recursive function calculations take so long in Mathematica?
    • From: Murray Eisenberg <murray@math.umass.edu>