“Jacobsthal Number”的概念、定义、习题解题方法及翻译-数学辞典

单词

Jacobsthal Number

释义

Jacobsthal Number

The Jacobsthal numbers are the numbers obtained by the s in the Lucas Sequence with and ,corresponding to and . They and the Jacobsthal-Lucas numbers (the s) satisfy the Recurrence Relation

(1)

The Jacobsthal numbers satisfy

and

and are 0, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, ... (Sloane's A001045).The Jacobsthal-Lucas numbers satisfy

and

and are 2, 1, 5, 7, 17, 31, 65, 127, 257, 511, 1025, ...(Sloane's A014551). The properties of these numbers are summarized in Horadam (1996). They are given by the closed formexpressions

			(2)
			(3)

where

is the Floor Function and

is a Binomial Coefficient. The Binet forms are

			(4)
			(5)

The Generating Functions are

(6)

(7)

The Simson Formulas are

(8)

(9)

Summation Formulas include

			(10)
			(11)

Interrelationships are

(12)

(13)

(14)

(15)

(16)

(17)

(18)

			(19)
			(20)

(21)

(22)

(23)

(24)

(25)

(26)

(27)

(28)

(29)

(30)

(31)

(Horadam 1996).

References

Horadam, A. F. ``Jacobsthal and Pell Curves.'' Fib. Quart. 26, 79-83, 1988.

Horadam, A. F. ``Jacobsthal Representation Numbers.'' Fib. Quart. 34, 40-54, 1996.

Sloane, N. J. A. SequencesA014551 andA001045/M2482in ``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.

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。