“Pell Number”的概念、定义、习题解题方法及翻译-数学辞典

单词

Pell Number

释义

Pell Number

The numbers obtained by the s in the Lucas Sequence with and . They and the Pell-Lucas numbers(the s in the Lucas Sequence) satisfy the recurrence relation

(1)

Using

to denote a Pell number and

to denote a Pell-Lucas number,

(2)

(3)

(4)

(5)

(6)

The Pell numbers have

and

and are 0, 1, 2, 5, 12, 29, 70, 169, 408, 985, 2378, ... (Sloane's A000129). The Pell-Lucas numbers have

and

and are 2, 2, 6, 14, 34, 82, 198, 478, 1154, 2786, 6726, ...(Sloane's A002203).

The only Triangular Pell number is 1 (McDaniel 1996).

See also Brahmagupta Polynomial, Pell Polynomial

References

McDaniel, W. L. ``Triangular Numbers in the Pell Sequence.'' Fib. Quart. 34, 105-107, 1996.

Sloane, N. J. A. SequencesA000129/M1413and A002203/M0360in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

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