nth Padovan Number

Return the Padovan sequence with P(0)=P(1)=P(2)=1 and P(n)=P(n−2)+P(n−3) as an exact decimal integer; the index is capped at 10,000.

Description

Padovan numbers add the terms two and three places earlier, skipping the immediately preceding term.

Padovan numbers add the terms two and three places earlier, skipping the immediately preceding term. The all-one initial triple fixes this sequence convention.^[1]

The tool returns value. The indexing and output conventions below determine how to read these values.

When to use nth Padovan Number

Use this for the following task: Return the Padovan sequence with P(0)=P(1)=P(2)=1 and P(n)=P(n−2)+P(n−3) as an exact decimal integer; the index is capped at 10,000. Use the input and output conventions below to reproduce the intended mathematical quantity.

How to use nth Padovan Number and understand its results

Choose the required indexes, integers or sequence entries. Preserve decimal-string encodings where the field table specifies strings.
Enter n according to the field table, then run the tool.
Read value. Preserve exact decimal strings and the stated indexing or coefficient order.
Keep exact decimal strings for subsequent integer arithmetic; distinguish them from any explicitly approximate numeric result.

Input field	Meaning	Value type and bounds	Requirement
n	Zero-indexed term (resource limit 10000)	integer; minimum 0; maximum 10000	Required

Maintain three BigInt values and shift them with next=a+b for n iterations. Return the selected zero-based term as decimal text.

P(0)=P(1)=P(2)=1; P(n)=P(n−2)+P(n−3)

The symbols and boundary conditions refer to the supplied fields and the implementation described above.

Output field	Meaning	Value type
value	Padovan number	string (integer/arbitrary)

json

{
  "input": {
    "n": 10
  },
  "output": {
    "value": "12"
  }
}

Limitations and assumptions

The index is at most 10000. Other starting triples are not supported, and the tool does not return the full prefix.

Use the declared integer bounds and string formats. Large exact outputs remain decimal strings; numerical approximations use ordinary floating-point arithmetic. A rejected input is different from a valid zero count or false membership flag.

Alternative or Complementary methods

Choose nth Tribonacci Number when you need its operation: Return T(n) exactly with T(0)=T(1)=0, T(2)=1, and each later term the sum of the preceding three; the index is capped at 10,000. Choose nth Pell Number for the complementary operation: Return P(n) exactly with P(0)=0, P(1)=1, and P(n)=2P(n−1)+P(n−2); the index is capped at 10,000.

Background reference: OEIS A000931.

References

OEIS A000931 — OEIS Foundation

Similar or alternative tools

nth Tribonacci Number
Return T(n) exactly with T(0)=T(1)=0, T(2)=1, and each later term the sum of the preceding three; the index is capped at 10,000.
nth Pell Number
Return P(n) exactly with P(0)=0, P(1)=1, and P(n)=2P(n−1)+P(n−2); the index is capped at 10,000.