[seqfan] Re: counting matrices by column rises

[Ron Hardin]

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/
> > 
> 
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