[seqfan] Re: counting matrices by column rises

[Ron Hardin]

I'll add the (extended) matrix and rows and columns 1-7 when it's finished.

 rhhardin at mindspring.com
rhhardin at att.net (either)



----- Original Message ----
> From: Neil Sloane <njasloane at gmail.com>
> To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> Sent: Mon, May 28, 2012 2:06:34 PM
> Subject: [seqfan] Re: counting matrices by column rises
> 
> Ron, Thanks for correcting and extending that sequence! I have edited
> A212806  accordingly. I also added a recurrence that they give for  these
> numbers.
> 
> In their notation, your 2-d array T(n,k) is their  R(k,n,0).
> 
> Could you possibly enter your array as a new sequence  (along
> with any rows and columns as you see fit)? (I would do it, but I  am
> a little short of time right now...)
> 
> Neil
> 
> On Sun, May 27,  2012 at 7:09 PM, Ron Hardin <rhhardin at att.net> wrote:
> 
> > An  independent method agrees with my a(1..8) so it is probably  right
> >
> >
> > 1 1
> > 2 3
> > 3 163
> > 4  271375
> > 5 21855093751
> > 6 128645361626874561
> > 7  78785944892341703819175577
> > 8  6795588328283070704898044776213094655
> > 9  107414633522643325764587104395687638119674465944431
> > 10  392471529081605251407320880492124164530148025908765037878553312273
> >  11
> >
> >  
>407934916447631403509359040563002566177814886353044858592046202746464825839911293037
>
> >
> >  12
> >
> >  
>145504642879259477281012058091622940407633028752039882958125884101920523620098689992011184443546760689025
>
> >
> >  13
> >
> >  
>21135271439464432464176935094829670293300173994858086117339990919638578785101112746033630102080750631173356200219659873152099061
>
> >
> >  14
> >
> >  
>1463431183893375284984759872630587182499184659625296120735012582497139747462114467290044676071057164230423617594882951286074571204260950002444632564792783
>
> >
> >  15
> >
> >  
>55886718275220893578836861232131886110904982213285838767171390268901523944185854477484902051056266062269027903116254642437898839626273376488836474974624509295801509147543849318171763
>
> >
> >  16
> >
> >  
>1348385569964624639358574892174460118889501498918522166832935200827715758081302249382041657004648509881448145286340717650181151030363404122918159081774157683623737791616797624376030976737382041097064975414203580415
>
> >
> >
> >  Doing the same problem for a nXk matrix you get T(n,k)  table
> >
> >
> >   .1...1.......1..........1.............1...............1...............1
> >  .1...3......19........211..........3651...........90921.........3081513
> >  .1...7.....163.......8983........966751.......179781181.....53090086057
> >  .1..15....1135.....271375.....158408751....191740223841.429966316953825
> >  .1..31....7291....7225951...21855093751.164481310134301................
> >  .1..63...45199..182199871.2801736968751................................
> >  .1.127..275563.4479288703..............................................
> >  .1.255.1666495.........................................................
> >  .1.511.................................................................
> >  .1.....................................................................
> >
> >  Row 2 is A000275
> >
> > rhhardin at mindspring.com
> > rhhardin at att.net (either)
> >
> >
> >
> > ----- Original Message ----
> >  > From: Ron Hardin <rhhardin at att.net>
> > > To:  Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > >  Sent: Sun, May 27, 2012 3:11:03 PM
> > > Subject: [seqfan] Re: counting  matrices by column rises
> > >
> > > I don't agree on a(5),  getting for a(1..8)
> > > 1 3 163 271375 21855093751   128645361626874561 78785944892341703819175577
> > >  6795588328283070704898044776213094655
> > >
> > > instead  of
> > >
> > > 1, 3, 163,  271375, 21855093749
> >  >
> > > The only check that my program is right, though, so  far,  is that the
> > first 4
> > > terms agree (and presumably is unlikely  to suddenly  go wrong at 5)
> > >
> > > I'll have to verify  it and put it on a faster  machine.
> > >
> > > rhhardin at mindspring.com
> > > rhhardin at att.net (either)
> >  >
> > >
> > >
> > > ----- Original Message ----
> >  > > From: Neil Sloane  <njasloane at gmail.com>
> > > >  To:  Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
> > >  > Sent:  Sun, May 27, 2012 2:29:45 PM
> > > > Subject:  [seqfan] counting matrices by  column rises
> > > >
> > >  > Dear SeqFans, I just discovered this interesting  paper:
> > >  > Abramson, Morton;  Promislow, David. Enumeration of arrays  by  column
> > rises.
> > > > J. Combinatorial  Theory Ser. A 24  (1978), no. 2,  247--250. MR0469773
> > (57
> > > >  #9554),
> > > > which led  me to add  A212805 and A212806 -  the latter needs more
> > terms.
> > Ron?
> > > >
> > >  > --
> > > > Dear Friends, I have now retired from AT&T. New  coordinates:
> > > >
> > > > Neil J.  A. Sloane,  President, OEIS Foundation
> > > > 11 South  Adelaide Avenue,  Highland  Park, NJ 08904, USA
> > > > Phone: 732 828 6098;   home page: http://NeilSloane.com
> > > > Email: njasloane at gmail.com
> > >  >
> > > >   _______________________________________________
> > > >
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> > >
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> >
> 
> 
> 
> -- 
> Dear Friends, I have  now retired from AT&T. New coordinates:
> 
> Neil J. A. Sloane, President,  OEIS Foundation
> 11 South Adelaide Avenue, Highland Park, NJ 08904,  USA
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
> 
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