Template:Sequence of the Day for September 17

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

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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.