Specific Names
The Lucas sequences for some values of P and Q have specific names:
- Un(1,−1) : Fibonacci numbers
- Vn(1,−1) : Lucas numbers
- Un(2,−1) : Pell numbers
- Vn(2,−1) : Companion Pell numbers or Pell-Lucas numbers
- Un(1,−2) : Jacobsthal numbers
- Vn(1,−2) : Jacobsthal-Lucas numbers
- Un(3, 2) : Mersenne numbers 2n − 1
- Vn(3, 2) : Numbers of the form 2n + 1, which include the Fermat numbers (Yubuta 2001).
- Un(x,−1) : Fibonacci polynomials
- Vn(x,−1) : Lucas polynomials
Some Lucas sequences have entries in the On-Line Encyclopedia of Integer Sequences:
-
1 1 A128834 A087204 1 2 A107920 -1 3 A214733 2 1 A001477 2 2 A009545 A007395 2 3 A088137 2 4 A008138 2 5 A045873 3 1 A001906 A005248 3 2 A000225 A000051 3 5 A190959 4 1 A001353 A003500 4 2 A056236 4 3 A003462 A034472 4 4 A001787 5 1 A003501
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