# Defining a recursive sequence

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

Am I doing something wrong?

## migrated from math.stackexchange.comMay 21 '12 at 5:17

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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:
G[y_]:=2G[y-1].

• 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]. – celtschk May 21 '12 at 8:17
• @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 ]] ? – user1952009 Sep 24 '16 at 14:20