# [seqfan] Re: Wavy Simple Recursion Involving Minimum

Dion Gijswijt d.c.gijswijt1 at uva.nl
Wed Jul 29 14:23:54 CEST 2009

```Because of the terms 0,1,2...,0,3,6,
it is clear that a(n+15)=3a(n) for all n, which gives a closed form
expression depending on n mod 15, right?

Dion.

On Wed, Jul 29, 2009 at 1:13 PM, Leroy Quet <q1qq2qqq3qqqq at yahoo.com> wrote:

>
> I just posted this:
>
> %I A163495
> %S A163495 0,1,2,2,1,1,2,1,1,3,4,3,0,3,3,0,3,6,6,3
> %V A163495 0,1,2,2,1,-1,-2,-1,1,3,4,3,0,-3,-3,0,3,6,6,3
> %N A163495 a(0)=0, a(1)=1, a(2)=2. For n>=3, a(n) = a(n-1) -
> min(a(n-2),a(n-3)).
> %K A163495 more,sign
> %O A163495 0,3
>
> Is there a closed (non-recursive) form for this sequence? (Maybe the closed
> form is involving, say, sine and the floor function. Or maybe the closed
> form is much simpler, maybe involving mod, say.)
>
> (And hopefully I didn't make a mistake figuring out the terms I submitted.)
>
> Thanks,
> Leroy Quet
>
> [ ( [ ([( [ ( ([[o0Oo0Ooo0Oo(0)oO0ooO0oO0o]]) ) ] )]) ] ) ]
>
>
>
>
>
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>

```