# 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

This question came from our site for people studying math at any level and professionals in related fields.

## 1 Answer

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

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

• 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. – Sjoerd C. de Vries May 21 '12 at 5:24
• 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:=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