[seqfan] Re: Looking for an interpretation

rkg rkg at ucalgary.ca
Wed Dec 23 21:25:59 CET 2015


I believe that I missed some earlier messages about this.

The sequence should start with 0 (=0*3) instead of 1.

The polynomial  x^4 - 2x^3 + 2x - 1 has roots 1,1,1,-1
so that the nth term is of shape

         (An^2 + Bn + C)*1^n + D(-1)^n

and in this case is

         (1/8)[2n^2 + 12n + 5(1 - (-1)^n)]

I have no combinatorial connexion.  How did it
arise?     R.

On Fri, 18 Dec 2015, Bruno Berselli wrote:

> I confirm the recurrence.
> Bruno 
>
>    Il Venerdì 18 Dicembre 2015 12:48, Ron Hardin <rhhardin at att.net> ha scritto:
> 
>
> a(n)=2*a(n-1)-2*a(n-3)+a(n-4) for n>5, apparently. rhhardin at mindspring.com rhhardin at att.net (either)
> 
>
> 
>       From: Peter Luschny <peter.luschny at gmail.com>
> To: "seqfan at list.seqfan.eu" <seqfan at list.seqfan.eu> 
> Sent: Friday, December 18, 2015 5:06 AM
> Subject: [seqfan] Looking for an interpretation
>   
> Consider the algorithm:
>
> x, y = 1, 2
> repeat:
>   print x
>   x, y = x + y, x//y + 1
>
> The assignment is simultaneous and x//y means floor(x/y).
> This leads to:
>
> 1, 3, 4, 8, 10, 15, 18, 24, 28, 35, 40, 48, 54, 63, 70, ...
>
> Can you contribute a combinatorial interpretation of this sequence?
>
> Cheers, Peter
>
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