I want to define a recursive sequence and then ask Mathematica to print a specific value:

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Am I doing something wrong?


1 Answer 1


First, you need to use "delayed substitution" so that Mathematica knows it needs to wait with evaluating expression until you type G[1]. Secondly, you can't have arithmetic expression on the left-hand side. so the second line should be:

  • 11
    $\begingroup$ y_ doesn't have anything to do with delayed substitution. It just means any argument (indicated by _), to be named y. If you leave away the underscore the call would work only for the literal symbol y. $\endgroup$ May 21, 2012 at 5:24
  • 6
    $\begingroup$ Also it's not strictly true that you can't have an arithmetic expression on the left hand side; it just gives completely different semantics from the one intended: The original definition would have been used when calling as G[y+1] (assuming y has no value assigned at the point of call). Indeed, when using a pattern, it can even make sense to have arithmetic arguments, e.g.: G[0]:=1;G[i_Integer/;i>0]:=2*G[i-1];G[y_+n_Integer/;n>0]:=2*G[y+n-1] Then you could write G[a+4] and get the result 16*G[a]. $\endgroup$
    – celtschk
    May 21, 2012 at 8:17
  • $\begingroup$ @celtschk Hi, could you explain if there is a difference between those two functions : H := Function[If[# <= 0, 0, H[# - 1] + #]] and G = Function[If[# <= 0, 0, r := G[# - 1] + #; r ]] ? $\endgroup$ Sep 24, 2016 at 14:20

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