Intended for: July 7, 2012
Timetable
- First draft entered by Alonso del Arte on March 12, 2011 based on an almost verbatim copy of a write-up by Daniel Forgues from November 12, 2010.
- First draft rejected because it is already being used for Sequence of the Day for July 2.
- New first draft entered by Alonso del Arte on April 30, 2011 mostly just copying comments made by John Blythe Dobson. ✓
- Draft reviewed by Daniel Forgues on May 5, 2011 ✓
- Draft approved by Alonso del Arte on July 6, 2011 ✓
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A000032:
Lucas numbers (beginning with
2)*:
L (n) = L (n − 1) + L (n − 2) |
with
.
-
{ 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, ... }
John Blythe Dobson connected some dots regarding Lucas and Fibonacci numbers:
The comments submitted by Miklos Kristof from Mar 19, 2007 for the Fibonacci numbers (A000045) contain four important identities which have close analogues in the Lucas numbers (A000204): For and odd , L (a + b) + L (a − b) = 5 F (a) F (b) |
. For and even , L (a + b) + L (a − b) = L (a) L (b) |
. For and odd , L (a + b) − L (a − b) = L (a) L (b) |
. For and even , L (a + b) − L (a − b) = 5 F (a) F (b) |
.
_______________
*
A000204 Lucas numbers (beginning with
1):
L (n) = L (n − 1) + L (n − 2) |
with
.