Padovan Sequence Calculator
Enter a number to see if it belongs to the Padovan Sequence, or input \( N \) to calculate the Nth term and its total sum.
What is the Padovan Sequence?
The Padovan Sequence is an integer sequence defined as follows:
- Initial terms: \( P(0) = P(1) = P(2) = 1 \)
- Recurrence relation: For \( n \geq 3 \), \( P(n) = P(n-2) + P(n-3) \)
How to Check if a Number Belongs to the Padovan Sequence
- Generate the Sequence: Compute Padovan Sequence terms using the recurrence relation until the generated value equals or exceeds the input number.
- Compare: Verify whether the input number exists in the generated sequence.
- Result: If the number is found, it belongs to the sequence; otherwise, it does not.
Examples
Example 1: Check if 5 Belongs to the Padovan Sequence
Solution:
Generate the sequence: 1, 1, 1, 2, 3, 4, 5.
Result: 5 is part of the Padovan Sequence.
Example 2: Check if 10 Belongs to the Padovan Sequence
Solution:
Generate the sequence: 1, 1, 1, 2, 3, 4, 5, 7, 9, 12.
Result: 10 is not part of the Padovan Sequence.
The First 100 Terms of the Padovan Sequence