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MathGroup Archive 1993

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Re: Recursive function

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Re: Recursive function
  • From: colinr at sue.econ.su.oz.au (Colin Rose)
  • Date: Tue, 28 Sep 93 2:35:30 EET

>>  I wish to define a recursive function with conditional special cases:
>>      f[n_, a_] := f[n-1,a] + f[n-1,a - n]  
>>
>>      s.t.:    (1) f[n,0] = 1     
>>               (2) If a<0 then f[n,a] = 0
>>               (3) If a >= n (n-1)/2 then f[n,a] = f[n,n(n+1)/2]
                    
One neat way of doing this is to use Which:

   f[n_, a_]  :=  Which[ a == 0,          1,
                         a < 0,           0, 
                         a >= n(n-1)/2,   f[n, n(n+1)/2],
                         True,            f[n-1, a] + f[n-1, a-n] ]

Regards

Colin

P.S. The function is 'non-convergent', as is clear from examining f[1, 1].

Colin Rose
Dept. of Economics
University of Sydney
colinr at extro.ucc.su.oz.au
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