[seqfan] Re: Looking for an interpretation

Bruno Berselli berselli.bruno at yahoo.it
Fri Dec 18 15:03:58 CET 2015


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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