# [seqfan] Re: Filling a triangle with numbers

Ron Hardin rhhardin at att.net
Fri Jul 6 16:31:10 CEST 2012

```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/
>

```