[seqfan] Re: Distances between points in Pascal's triangle

[franktaw at netscape.net]

 A very naive analysis:

To get an even distance, both x-y and y-z must be even.
To get an odd distance, one must be even and the other odd.
So one would expect twice as many odd values as even.

Franklin T. Adams-Watters
 

-----Original Message-----
From: Charles Greathouse <charles.greathouse at case.edu>

Consider three consecutive binomial coefficients in Pascal's triangle x =
binomial(n, k), y = binomial(n,k+1), and z = binomial(n, k+2) such that the
distance sqrt((x-y)^2 + (y-z)^2) between (x, y) and (y, z) is an integer.

J. M. Bergot poses this question: why is n so often odd rather than even?

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

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