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July 11th, 2011, 01:57 PM   #1
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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.
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July 11th, 2011, 02:08 PM   #2
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Re: recursive definitions

So what have you come up with so far, and where exactly you seem to be stuck in?
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July 11th, 2011, 02:37 PM   #3
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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.
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July 12th, 2011, 08:39 AM   #4
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Re: recursive definitions

I'm partial to a(n) = a(n-4) for #1, but I suspect that the desired answer is more like a(n) = k * a(n-1). What value of k can you choose to make this true? (This is related to Hooman's hint.)
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July 13th, 2011, 03:02 PM   #5
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Re: recursive definitions

for a) I got

f(0) = 2
f(n+1) = f(n) x 5

could that work?
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July 13th, 2011, 04:00 PM   #6
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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
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July 14th, 2011, 08:32 AM   #7
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Re: recursive definitions

Quote:
Originally Posted by lamhmh
for a) I got

f(0) = 2
f(n+1) = f(n) x 5

could that work?
Correct!
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July 14th, 2011, 08:46 AM   #8
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Re: recursive definitions

Quote:
Originally Posted by lamhmh
the number of ways to stack n red, white, green and blue poker chips so that there are no two consecutive blue poker chips
Step 1: stack the red, white, and green chips.
Step 2: decide where to insert the blue chips. If there are n-b chips already stacked, there are n-b+1 places to choose from.
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