Difference between revisions of "T(n)^2=T(T(n))+T(T(n)-1)"

From specialfunctionswiki
Jump to: navigation, search
 
(2 intermediate revisions by the same user not shown)
Line 1: Line 1:
 
==Theorem==
 
==Theorem==
 
The following formula holds for $n=2,3,4,\ldots$:
 
The following formula holds for $n=2,3,4,\ldots$:
$$T(n)^2=T(T(n))+T(T(n-1)),$$
+
$$T(n)^2=T(T(n))+T(T(n)-1),$$
 
where $T(n)$ denotes the $n$th [[triangular numbers|triangular number]].
 
where $T(n)$ denotes the $n$th [[triangular numbers|triangular number]].
  
Line 7: Line 7:
  
 
==References==
 
==References==
* {{PaperReference|Triangular numbers|1974|V.E. Hoggatt, Jr|author2=Marjorie Bicknell|prev=N^2=T(n)+T(n-1)|next=findme}}
+
* {{PaperReference|Triangular numbers|1974|V.E. Hoggatt, Jr|author2=Marjorie Bicknell|prev=N^2=T(n)+T(n-1)|next=T(n+1)^2-T(n)^2=(n+1)^3}} $(1.4)$
  
 
[[Category:Theorem]]
 
[[Category:Theorem]]
 
[[Category:Unproven]]
 
[[Category:Unproven]]

Latest revision as of 01:30, 30 May 2017

Theorem

The following formula holds for $n=2,3,4,\ldots$: $$T(n)^2=T(T(n))+T(T(n)-1),$$ where $T(n)$ denotes the $n$th triangular number.

Proof

References