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Given a number n, find the nth number in the Padovan Sequence.A Padovan Sequence is a sequence which is represented by the following recurrence relationP(n) = P(n-2) + P(n-3)P(0) = P(1) = P(2) = 1Note: Since the output may be too large, compute the answer modulo 10^9+7.

Question

Given a number n, find the nth number in the Padovan Sequence.A Padovan Sequence is a sequence which is represented by the following recurrence relationP(n) = P(n-2) + P(n-3)P(0) = P(1) = P(2) = 1Note: Since the output may be too large, compute the answer modulo 10^9+7.

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Solution

Here is a step-by-step solution to find the nth number in the Padovan Sequence:

  1. Initialize an array P of size n+1 to store the Padovan sequence. Set P[0], P[1] and P[2] to 1, as given in the problem.

  2. For i from 3 to n, compute P[i] as P[i-2] + P[i-3]. This is based on the recurrence relation given in the problem.

  3. Since the output may be too large, compute the answer modulo 10^9+7 at each step. This can be done by replacing the computation in step 2 with P[i] = (P[i-2] + P[i-3]) % (10^9+7).

  4. After the loop, P[n] will be the nth number in the Padovan sequence.

Here is a Python code snippet that implements the above steps:

def padovan(n):
    P = [1, 1, 1] + [0]*n
    mod = 10**9+7
    for i in range(3, n+1):
        P[i] = (P[i-2] + P[i-3]) % mod
    return P[n]

You can call this function with a specific n to get the nth number in the Padovan sequence. For example, padovan(5) will return 2, which is the 5th number in the sequence.

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Similar Questions

Write a Python program using functions and recursion to generate and display the first 15 numbers of the Padovan sequence. The Padovan sequence begins with the first three terms as 1, 1, and 1, and each subsequent term is the sum of the previous two terms. For example, the first few terms of the Padovan sequence are: 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37,.Note: The Padovan sequence is a sequence of numbers similar to the Fibonacci sequence, where each term is the sum of the previous two terms.

Choose the 10th term of the sequence with the nth term as

Instead of storing the entire Padovan sequence in a list, you can optimize the space complexity by just storing the last three elements of the sequence. This way, you can calculate the next element based on these three elements without storing the entire sequence.

What is the next number in the sequence below?10     13     9     14     81522167

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Here are the nth terms of 4 sequences.Sequence 1 nth term 3n + 1Sequence 2 nth term 5n + 10Sequence 3 nth term 10nSequence 4 nth term 5n - 1For each sequence state whether the numbers in the sequence areA Always multiples of 5S Sometimes multiples of 5N Never multiples of 5Sequence 1 ....................Sequence 2 ....................Sequence 3 ....................Sequence 4 ....................(4)Page 8 of 1111. The nth term of a sequence is 5 − 3nWrite down the first three terms of the sequence.1st term ..............., 2nd term ..............., 3rd term ...............(2)12. The nth term of a sequence is 4n − 7(a) Write down the first three terms of the sequence.1st term ..............., 2nd term ..............., 3rd term ...............(2)(b) What is the difference between the 50th and 51st terms?....................(1)The last term of this sequence is 393.(c) How many terms are there in this sequence?....................(2)Page 9 of 1113. 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