1
$\begingroup$

Suppose that you have a large supply of red, white, green and blue poker chips. you want to make a vertical stack of n chips in such a way that the stack does not contain any consecutive blue chips.

Find a recurrence relation for $a_n$ where $ a_n$ denotes the number of ways you can make such a stack of n poker chips.

Blue chip first then i have 3 choices for next chip of the n-2 remaining symbols i write ($ a_{n-2} $)?

for the second case where blue is not the first chip simply let ( $a_{n-1} $ ) be the Operation? symbol? function? i dont know on the remaining n-1 symbols.

$a_n = 3( a_{n-1} )+ 3( a_{n-2} ) $

Does this result make any sense?

$\endgroup$
5
  • 1
    $\begingroup$ The result aside, the way in which you wrote the result and your thoughts makes little to no sense. In any case, note that a stack with no consecutive blue chips will either have a non-blue chip at the top (and what below that?) or will have a blue chip at the top and a non-blue chip second from the top (and what below that?) $\endgroup$
    – JMoravitz
    Mar 28, 2017 at 19:47
  • $\begingroup$ ? thats what i wrote Blue chip then 3 choices then n-2. not blue chip at the top then n-1 satisfies the remaining result? $\endgroup$
    – Faust
    Mar 28, 2017 at 19:49
  • $\begingroup$ You seem to see what is going on correctly., my point is that looking at this without any context, we'd see a line in which you wrote "B3$a_{n-2}$" and not have any idea what you are meaning to say. Using enough words to make it clear will help. $\endgroup$
    – JMoravitz
    Mar 28, 2017 at 19:51
  • $\begingroup$ i dont know a better format to communicate what im thinking ill try looking at the format of how others have solved reccurence relations then try editing it. $\endgroup$
    – Faust
    Mar 28, 2017 at 19:51
  • $\begingroup$ I think the fact that i have no idea what im doing is adding a layer of confusion to what im supposed to write... im just trying to break it into cases and then use the _____ word i dont know to piece the recurrence together cause the example in my textbook does that. $\endgroup$
    – Faust
    Mar 28, 2017 at 20:00

1 Answer 1

1
$\begingroup$

Just add some helpful definitions:

Define $r_n$ as any sequence ending in red, white, or green.

Define $b_n$ as any sequence ending in blue.

Obviously $a_n = b_n + r_n$, and your reasoning to find $r_n$ and $b_n$ is correct.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.