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
Read more about this topic: Lucas Sequence
Famous quotes containing the words specific and/or names:
“In effect, to follow, not to force the public inclination; to give a direction, a form, a technical dress, and a specific sanction, to the general sense of the community, is the true end of legislature.”
—Edmund Burke (1729–1797)
“Shut out that stealing moon,
She wears too much the guise she wore
Before our lutes were strewn
With years-deep dust, and names we read
On a white stone were hewn.”
—Thomas Hardy (1840–1928)