• 1 Vote(s) - 5 Average
• 1
• 2
• 3
• 4
• 5
 My favorite integer sequence Gottfried Ultimate Fellow Posts: 789 Threads: 121 Joined: Aug 2007 08/02/2014, 09:29 PM (This post was last modified: 08/03/2014, 10:15 AM by Gottfried.) One more contribution. Let as in the previous post $w(x)$ be the generating function for the original sequence A $(1,1,2,2,4,4,6,6,10,10,...)$ . Now we look at the sequences $A_k$ for which the powers $w(x)^k$ are the generating functions. In the previous posts I'd already pointed to that of k=-1 where the sequence $A_{-1}$ is the "ubiquitueous Thue-Morse-sequence". First a list of the sequences. Left column is for $w(x)^{-3}$ , then for k=-2,-1,0,1 (which gives the column with our sequence under discussion), then k=2,3,4:     Now the matrices, for which that sequences are the "eigen-sequences". Their generating follows a very simple pattern. I always show the matrix $M_k$ and the associated sequence $A_k$ together: (for sequence and more information see http://oeis.org/A106407 )     (for sequence and more information see http://oeis.org/A106400 )         (for sequence and more information see http://oeis.org/A018819 )     Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Messages In This Thread My favorite integer sequence - by tommy1729 - 07/27/2014, 08:44 PM RE: My favorite integer sequence - by jaydfox - 07/31/2014, 01:51 AM RE: My favorite integer sequence - by jaydfox - 08/01/2014, 01:53 AM RE: My favorite integer sequence - by Gottfried - 08/01/2014, 03:25 PM RE: My favorite integer sequence - by jaydfox - 08/01/2014, 05:04 PM RE: My favorite integer sequence - by sheldonison - 08/01/2014, 11:36 PM RE: My favorite integer sequence - by jaydfox - 08/01/2014, 11:57 PM RE: My favorite integer sequence - by jaydfox - 08/05/2014, 04:49 PM RE: My favorite integer sequence - by jaydfox - 08/05/2014, 05:57 PM RE: My favorite integer sequence - by Gottfried - 08/06/2014, 04:38 PM RE: My favorite integer sequence - by jaydfox - 08/07/2014, 01:19 AM RE: My favorite integer sequence - by jaydfox - 08/07/2014, 01:34 AM RE: My favorite integer sequence - by jaydfox - 08/09/2014, 09:42 AM RE: My favorite integer sequence - by Gottfried - 08/09/2014, 02:27 PM RE: My favorite integer sequence - by tommy1729 - 09/09/2014, 12:55 AM RE: My favorite integer sequence - by jaydfox - 08/08/2014, 12:55 AM RE: My favorite integer sequence - by Gottfried - 08/08/2014, 02:27 AM RE: My favorite integer sequence - by jaydfox - 09/09/2014, 07:43 PM RE: My favorite integer sequence - by jaydfox - 09/09/2014, 09:45 PM RE: My favorite integer sequence - by jaydfox - 08/02/2014, 12:08 AM RE: My favorite integer sequence - by tommy1729 - 08/03/2014, 11:38 PM RE: My favorite integer sequence - by sheldonison - 08/04/2014, 11:49 PM RE: My favorite integer sequence - by jaydfox - 09/16/2014, 05:32 AM RE: My favorite integer sequence - by Gottfried - 09/17/2014, 07:39 PM RE: My favorite integer sequence - by jaydfox - 10/02/2014, 10:53 PM RE: My favorite integer sequence - by Gottfried - 08/03/2014, 03:32 PM RE: My favorite integer sequence - by tommy1729 - 08/03/2014, 11:44 PM RE: My favorite integer sequence - by sheldonison - 08/02/2014, 05:48 AM RE: My favorite integer sequence - by tommy1729 - 09/10/2014, 08:57 PM RE: My favorite integer sequence - by Gottfried - 08/02/2014, 07:43 PM RE: My favorite integer sequence - by Gottfried - 08/02/2014, 09:29 PM RE: My favorite integer sequence - by Gottfried - 08/02/2014, 09:36 PM RE: My favorite integer sequence - by tommy1729 - 08/05/2014, 11:16 PM RE: My favorite integer sequence - by tommy1729 - 08/08/2014, 11:02 PM RE: My favorite integer sequence - by jaydfox - 08/09/2014, 07:02 PM RE: My favorite integer sequence - by jaydfox - 08/09/2014, 10:51 PM RE: My favorite integer sequence - by sheldonison - 08/11/2014, 04:51 PM RE: My favorite integer sequence - by jaydfox - 08/11/2014, 05:19 PM RE: My favorite integer sequence - by jaydfox - 08/19/2014, 01:36 AM RE: My favorite integer sequence - by jaydfox - 08/19/2014, 02:05 AM RE: My favorite integer sequence - by jaydfox - 08/19/2014, 05:31 PM RE: My favorite integer sequence - by sheldonison - 08/19/2014, 07:56 PM RE: My favorite integer sequence - by jaydfox - 08/20/2014, 07:42 AM RE: My favorite integer sequence - by sheldonison - 08/20/2014, 02:11 PM RE: My favorite integer sequence - by jaydfox - 08/20/2014, 07:57 PM RE: My favorite integer sequence - by jaydfox - 08/21/2014, 01:15 AM RE: My favorite integer sequence - by jaydfox - 08/21/2014, 05:25 AM RE: My favorite integer sequence - by jaydfox - 08/22/2014, 05:39 PM RE: My favorite integer sequence - by jaydfox - 09/11/2014, 01:33 AM RE: My favorite integer sequence - by tommy1729 - 08/09/2014, 09:16 PM RE: My favorite integer sequence - by jaydfox - 08/09/2014, 10:19 PM RE: My favorite integer sequence - by tommy1729 - 08/09/2014, 10:52 PM RE: My favorite integer sequence - by jaydfox - 08/09/2014, 11:46 PM RE: My favorite integer sequence - by tommy1729 - 08/09/2014, 11:10 PM RE: My favorite integer sequence - by jaydfox - 08/10/2014, 12:30 AM RE: My favorite integer sequence - by tommy1729 - 08/11/2014, 12:17 PM RE: My favorite integer sequence - by Gottfried - 08/22/2014, 12:30 AM Amazing variant - by tommy1729 - 08/26/2014, 08:57 PM RE: My favorite integer sequence - by tommy1729 - 09/01/2014, 10:37 PM RE: My favorite integer sequence - by tommy1729 - 10/02/2014, 11:24 PM RE: My favorite integer sequence - by jaydfox - 10/02/2014, 11:29 PM RE: My favorite integer sequence - by tommy1729 - 02/10/2015, 12:15 AM RE: My favorite integer sequence - by tommy1729 - 02/15/2015, 05:19 PM RE: My favorite integer sequence - by tommy1729 - 10/07/2015, 08:22 AM RE: My favorite integer sequence - by tommy1729 - 10/07/2015, 09:10 PM RE: My favorite integer sequence - by tommy1729 - 03/13/2016, 12:31 AM

 Possibly Related Threads... Thread Author Replies Views Last Post My favorite theorem tommy1729 0 4,115 08/15/2015, 09:58 PM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)