For n 1, in how many out of the n! permutations = ((1), (2).....(n)) of...

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For n ≥ 1, in how many out of the n! permutations = ((1), (2).....(n)) of the numbers (1,2,...,n} the value of x(i) is either i-1, or i, or i+ 1 for all 1 ≤ i ≤n? Example: The permutation (21354) follows the rules while the permutation (21534) does not because (3) = 5. Hint: Find the answer for small n by checking all the permutations and then find the recursive formula depending on the possible values for (n). For n ≥ 1, in how many out of the n! permutations = ((1), (2).....(n)) of the numbers (1,2,...,n} the value of x(i) is either i-1, or i, or i+ 1 for all 1 ≤ i ≤n? Example: The permutation (21354) follows the rules while the permutation (21534) does not because (3) = 5. Hint: Find the answer for small n by checking all the permutations and then find the recursive formula depending on the possible values for (n).

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To determine how many permutations of the numbers 1 2 n follow the rules where i is either i1 i or i... View the full answer