# [seqfan] Re: (no subject)

Raff, Paul praff at math.rutgers.edu
Mon Nov 9 16:52:34 CET 2009

```Hi Ctibor,

I think you mean the following (with modification in caps):

a(n)= ceiling(SQRT(n*(n+1)/2))^2 - n*(n+1)/2

[paul]

---
Paul Raff
Postdoctoral Researcher - Cognitive Assistants as Analysts' Deputies
School of Communication and Information
Rutgers University
http://www.myraff.com
Work: (732) 932-7500 x8023
Mobile: (704) 604-2154
---

On Mon, Nov 9, 2009 at 10:42 AM, <c.zizka at email.cz> wrote:

> Dear seqfans,
>
> let a(n) is the difference between n-th triangular number and next perfect
> square (submitted to OEIS today).
>
> a(n)= (ceiling(n*(n+1)/2))^2 - n*(n+1)/2
>
> Interestingly a(n) takes values {0,1,3,4,6,8,9,10,13,15,16,19,21,22,...}
> and it seems no a(n) is from {2,5,7,11,12,14,17,18,20,23,...} .
> In OEIS we can found for a(n)=0   A001108, for a(n)=1  A006451, for a(n)=3
>  A154138,  for a(n)=4  A154139 , for a(n)=6  A154140, for a(n)=8  A154141,
> for a(n)=9   A154142, for a(n)=10  A154143.
>
> Why can not be :
>
>  (ceiling(n*(n+1)/2))^2  =  2+ n*(n+1)/2
>
> :-)
>
> Ctibor
>
>
>
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>

```