[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/
> >
>
> _______________________________________________
>
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>
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