[seqfan] Filling a triangle with numbers
Neil Sloane
njasloane at gmail.com
Fri Jul 6 15:51:07 CEST 2012
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
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