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Template:Sequence of the Day for September 17

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Intended for: September 17, 2011

Timetable

  • First draft entered by Alonso del Arte on September 4, 2011
  • Draft reviewed by Daniel Forgues on September 17, 2012
  • Draft to be approved by August 17, 2011
Yesterday's SOTD * Tomorrow's SOTD

The line below marks the end of the <noinclude> ... </noinclude> section.



A156090: Alternating sum of the squares of the first
n
Fibonacci numbers with index divisible by 3.
{ 0, − 4, 60, −1096, 19640, −352460, ... }

As is the case with many sequences derived from the Fibonacci numbers, this one can be expressed in quite a few different ways, e.g. as a sum

a (n)  = 
n
k  = 1
  (−1)k F  (3k ) 2
,
where for
n = 0
we get the empty sum, i.e. 0, or with a closed formula
a (n)  =  (−1)n
F  (6 n + 3)
10
 − 
2 n + 1
5
 ,

to name just two.