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Template:Sequence of the Day for August 2

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Intended for: August 2, 2012

Timetable

  • First draft entered by Alonso del Arte on June 1, 2011 as a verbatim copy of a write-up from December 2, 2010. ✓
  • Draft reviewed by Alonso del Arte on June 3, 2011 ✓, and by Daniel Forgues on August 1, 2018
  • Draft approved by Daniel Forgues on July 2, 2011
Yesterday's SOTD * Tomorrow's SOTD

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



A007598:
Fn 2
, squares of the Fibonacci numbers.
{ 1, 1, 4, 9, 25, 64, 169, 441, ... }
In the Fibonacci multiplication table, this sequence is in a very predictable diagonal. But closer inspection of the table yields an interesting formula for this sequence:
Fn 2 = Fn  − i Fn  + i + ( − 1)n  + i Fi   2
. But this is just scratching the tip of the iceberg.
Fibonacci multiplication triangle
T (n, k) = Fn Fk , n   ≥   1, 1   ≤   k   ≤   n.
Row sums
Fn (Fn +2  −  1), n   ≥   1.

A143212
                     
1 1
1 1 2
2 2 4 8
3 3 6 9 21
5 5 10 15 25 60
8 8 16 24 40 64 160