Euler Zigzag numbers is a sequence of integers which is a number of arrangements of those numbers so that each entry is alternately greater or less than the preceding entry.
c1, c2, c3, c4 is Alternating permutation where
c1 < c2
c3 < c2
c3 < c4…
zigzag numbers are as follows 1, 1, 1, 2, 5, 16, 61, 272, 1385, 7936, 50521 ……
For a given integer N. The task is to print sequence up to N terms.
Input : N = 10
Output : 1 1 1 2 5 16 61 272 1385 7936
Input : N = 14
Output : 1 1 1 2 5 16 61 272 1385 7936 50521 353792 2702765 22368256
The (n+1)th Zigzag number is :
We will find the factorial upto n and store them in an array and also create a second array to store the i th zigzag number and apply the formula stated above to find all the n zigzag numbers.
Below is the implementation of the above approach :
zig zag numbers: 1 1 1 2 5 16 61 272 1385 7936
- Euler's Totient function for all numbers smaller than or equal to n
- Find a permutation of 2N numbers such that the result of given expression is exactly 2K
- Find the good permutation of first N natural numbers
- Find permutation of first N natural numbers that satisfies the given condition
- Find the number of sub arrays in the permutation of first N natural numbers such that their median is M
- Minimum number of given operations required to convert a permutation into an identity permutation
- Euler's Totient Function
- Euler's Four Square Identity
- Euclid Euler Theorem
- Minimum number of replacements to make the binary string alternating | Set 2
- Euler Method for solving differential equation
- Total nodes traversed in Euler Tour Tree
- Count integers in a range which are divisible by their euler totient value
- Optimized Euler Totient Function for Multiple Evaluations
- Euler's criterion (Check if square root under modulo p exists)
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.