Template:Sequence of the Day for August 2

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