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.
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