What is the recurrence formula for #K_n#? #K_n# is the number of strings (#a_1,a_2,...,a_n) with words from set {0, 1, 2} under the following conditions.
This problem is originally asked by @smkwd.
https://socratic.org/questions/how-to-prove-that#484241
I divided it into smaller parts so as to avoid getting the answer too long.
--Here is the divided question--
Consider a string (#a_1,a_2,...,a_n# ) with words from set {0, 1, 2}.
We will call the pod of the character (#a_i,a_(i+1),. . . a_j# ), where #1≤i≤j≤n# and #a_i = a_(i + 1) =. . . = a_j# . The block is called maximum if it is not contained in no longer block. For example, in string (1, 0, 0, 2, 1, 1) the maximum blocks are (1), (0, 0), (2), (1, 1).
Let #K_n# be the number of such lengths #n# of words from the set {0, 1, 2} in which all maximal blocks have odd lengths.
What is the recurrence formula #K_n# satisfies?
This problem is originally asked by @smkwd.
https://socratic.org/questions/how-to-prove-that#484241
I divided it into smaller parts so as to avoid getting the answer too long.
--Here is the divided question--
Consider a string (
We will call the pod of the character (
Let
What is the recurrence formula
1 Answer
Explanation:
First we have to find
Then, what do we need to calculate
Three words strings to have every maximum blocks odd words are categorized into two types.
Strings like
Strings like
This pattern continues for every
The recurrence formula