Problem 46037. Count alternating permutations

ChrisR

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In an alternating permutation of numbers 1 to n, the numbers are arranged so that they alternately increase and decrease. For example, there are five alternating permutations of the numbers 1, 2, 3, and 4:
 1 3 2 4
 1 4 2 3
 2 3 1 4
 2 4 1 3
 3 4 1 2
Write a function to count the alternating permutations for a set of n numbers.
Suggestion: You might also try Cody Problem 46034.

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21 Solutions

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Last Solution submitted on Sep 29, 2026

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Tim on 10 Jul 2020

The test case result for n=5 seems a tad high.

ChrisR on 10 Jul 2020

Tim, that last case is altperm(altperm(5)). I did that to discourage lookup solutions.

Tim on 10 Jul 2020

Oops--my mistake.

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