Lucas n-Step Number
المؤلف:
Sloane, N. J. A.
المصدر:
Sequences A000204/M2341, A001644/M2625, A0016482648, and A023424 in "The On-Line Encyclopedia of Integer Sequences."
الجزء والصفحة:
...
7-12-2020
1518
Lucas n-Step Number
An 
-step Lucas sequence ![<span style=]()
{L_k^((n))}_(k=1)^infty" src="https://mathworld.wolfram.com/images/equations/Lucasn-StepNumber/Inline2.gif" style="height:22px; width:49px" /> is defined by letting 
for 
, 
, and other terms according to the linear recurrence equation
for 
.
The first few sequences of 
-step Lucas numbers are summarized in the table below.
 |
OEIS |
 ,  , ... |
| 2 |
A000204 |
1, 3, 4, 7, 11, 18, 29, 47, 76, 123, ... |
| 3 |
A001644 |
1, 3, 7, 11, 21, 39, 71, 131, 241, 443, ... |
| 4 |
A001648 |
1, 3, 7, 15, 26, 51, 99, 191, 367, 708, ... |
| 5 |
A023424 |
1, 3, 7, 15, 31, 57, 113, 223, 439, 863, ... |
REFERENCES:
Noe, T. D. and Post, J. V. "Primes in Fibonacci 
-step and Lucas 
-Step Sequences." J. Integer Seq. 8, Article 05.4.4, 2005. https://www.cs.uwaterloo.ca/journals/JIS/VOL8/Noe/noe5.html.
Sloane, N. J. A. Sequences A000204/M2341, A001644/M2625, A0016482648, and A023424 in "The On-Line Encyclopedia of Integer Sequences."
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