The companion Pell numbers or Pell-Lucas numbers are defined by the recurrence relation
In words: the first two numbers in the sequence are both 2, and each successive number is formed by adding twice the previous Pell-Lucas number to the Pell-Lucas number before that, or equivalently, by adding the next Pell number to the previous Pell number: thus, 82 is the companion to 29, and 82 = 2 * 34 + 14 = 70 + 12. The first few terms of the sequence are (sequence A002203 in OEIS): 2, 2, 6, 14, 34, 82, 198, 478...
The companion Pell numbers can be expressed by the closed form formula
These numbers are all even; each such number is twice the numerator in one of the rational approximations to discussed above.
Read more about this topic: Pell Number
Famous quotes containing the word numbers:
“Old age equalizes—we are aware that what is happening to us has happened to untold numbers from the beginning of time. When we are young we act as if we were the first young people in the world.”
—Eric Hoffer (1902–1983)