[seqfan] Re: Filling a triangle with numbers

[Neil Sloane]

And indeed this is one of the alternative definitions of A003121!
Ron, Thanks!


On Fri, Jul 6, 2012 at 10:31 AM, Ron Hardin <rhhardin at att.net> wrote:

> sequence starts   1  1  2  12  286
> which matches A003121
>
>  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: Fri, July 6, 2012 10:18:38 AM
> > Subject: [seqfan] Re: Filling a triangle with numbers
> >
> > I get 12 for  a(4)
> > .....5........6........6........5........5........3........3........4..
> > ....3.7......3.7......2.7......2.7......3.6......2.6......2.7......3.7..
> > ...1.4.8....1.4.8....1.4.8....1.4.8....1.4.8....1.5.8....1.5.8....1.5.8..
> >
> ..0.2.6.9..0.2.5.9..0.3.5.9..0.3.6.9..0.2.7.9..0.4.7.9..0.4.6.9..0.2.6.9..
> > ..
> > .....4........4........5........4..
> > ....2.6......2.7......2.6......3.6..
> > ...1.5.8....1.5.8....1.4.8....1.5.8..
> > ..0.3.7.9..0.3.6.9..0.3.7.9..0.2.7.9..
> >
> > 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:  Fri, July 6, 2012 9:51:14 AM
> > > Subject: [seqfan] Filling a triangle with  numbers
> > >
> > > I heard this problem in Hungary recently:
> > >
> > > How many ways are there to  arrange the numbers 1 through n(n+1)/2  in
> > > a triangle so that each term is  between the two numbers
> > >  immediately below it (and each row is  increasing)?
> > >
> > >  Examples:
> > > .2.
> > > 1.3
> > >
> > > ..4..
> > > .2.5.
> > >  1.3.6
> > >
> > > ..3..
> > > .2.5.
> > > 1.4.6
> > >
> > >  I  get a(1)=a(2)=1, a(3)=2, a(4)=6?
> > >
> > > The only related  sequences I can find  in the OEIS are A064049,
> A064059,
> > > which are  different. However, it is quite  likely this is a
> well-studied
> > >  problem.
> > >
> > > Also, what if one omits the  clause in  parentheses in the  definition?
> > >
> > > Neil
> > >
> > >  _______________________________________________
> > >
> > > Seqfan   Mailing list - http://list.seqfan.eu/
> > >
> >
> > _______________________________________________
> >
> > Seqfan Mailing  list - http://list.seqfan.eu/
> >
>
> _______________________________________________
>
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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