[seqfan] Re: counting matrices by column rises

[Neil Sloane]

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
> > >
> > >  _______________________________________________
> > >
> > > Seqfan   Mailing list - http://list.seqfan.eu/
> > >
> >
> > _______________________________________________
> >
> > Seqfan Mailing  list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
> Seqfan Mailing list - http://list.seqfan.eu/
>



-- 
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