July 11th, 2011, 01:57 PM  #1 
Member Joined: May 2011 Posts: 38 Thanks: 0  recursive definitions
construct a recursive definition for each: a) the sequence 2, 10, 50, 250... b) the number of ways a sequence of 1's and 2's will sum to n. For example, x3 = 3 since 2+1, 1+1+1, and 1+2 all sum to 3. Notice that 1+2 is not the same as 2+1, since the first and second elements of each sum are different c) the number of ways to stank n red, white, green, and blue poker chips so that there are no two consecutive blue poker chips. 
July 11th, 2011, 02:08 PM  #2 
Senior Member Joined: Jan 2011 Posts: 106 Thanks: 0  Re: recursive definitions
So what have you come up with so far, and where exactly you seem to be stuck in?

July 11th, 2011, 02:37 PM  #3 
Senior Member Joined: Jul 2011 Posts: 227 Thanks: 0  Re: recursive definitions
For example exercice a): Important here is to examine if these sequence is arithmetic or geometric, if you know that you'Il be able to construct a recursive formula. 
July 12th, 2011, 08:39 AM  #4 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: recursive definitions
I'm partial to a(n) = a(n4) for #1, but I suspect that the desired answer is more like a(n) = k * a(n1). What value of k can you choose to make this true? (This is related to Hooman's hint.)

July 13th, 2011, 03:02 PM  #5 
Member Joined: May 2011 Posts: 38 Thanks: 0  Re: recursive definitions
for a) I got f(0) = 2 f(n+1) = f(n) x 5 could that work? 
July 13th, 2011, 04:00 PM  #6 
Member Joined: May 2011 Posts: 38 Thanks: 0  Re: recursive definitions
i can't seem to find the sequence for the last one: the number of ways to stack n red, white, green and blue poker chips so that there are no two consecutive blue poker chips 
July 14th, 2011, 08:32 AM  #7  
Senior Member Joined: Jul 2011 Posts: 227 Thanks: 0  Re: recursive definitions Quote:
 
July 14th, 2011, 08:46 AM  #8  
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: recursive definitions Quote:
Step 2: decide where to insert the blue chips. If there are nb chips already stacked, there are nb+1 places to choose from.  

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