[seqfan] Re: Filling a triangle with numbers
Olivier Gerard
olivier.gerard at gmail.com
Fri Jul 6 17:12:41 CEST 2012
Dear Neil,
I evidently confirm Ron's numbers. A003121 is what you were looking for.
If one does not require increasing rows, (i.e. the top number is between
[min() , max()]
of the two numbers below the sequence starts
1, 2, 20, 1744, ... (apparently not in the OEIS)
If one does not require that a number be used only one time, but with strict
inequality, and increasing rows, the sequence starts
1, 1, 8, ...
If one does not require increasing rows or unique use, the sequence starts
1, 2, 104, ...
Olivier
On Fri, Jul 6, 2012 at 4:31 PM, 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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