Re: question on fitting a function to an actual distribution

On 2025-11-27 01:53, American Citizen wrote:

 > I have been pushing forward, using a function in gp-pari script 
written by Max Alekseyev, which finds how many sets of square triads 
might sum to a given number. For example n=194 results in [[0, 5, 13], 
[1, 7, 12], [3, 4, 13], [3, 8, 11], [5, 5, 12], [7, 8, 9]] or six 
triads, the number 194 is the smallest for 6 triads. His program works 
very well, and I verified it for the values of 1 <= n <= 1e7. (first 240 
values of rel max highs)
 >
 > I have a collection of 41,374 triad counts for the 1 <= count <= 
41374 with the n value given.
 > This distribution seems to follow:
 > (1)  n =  5.32459104391076 * count ^ 1.93934231682073
 > which is a linear graphic when plotted on a log-log scale.

Power Law :)
https://www.youtube.com/watch?v=HBluLfX2F_k (Veritasium)


 > But at the very first the distribution curiously drops below (1) for 
the first dozen or two dozen values.
 > Would anyone be curious to find a better fit for the value of n 
versus the count value of square triads? I am happy to send you the 
41374 row file of currently determined values, for testing purposes.

Maybe also ask on the seqfan mailing list.

 > "the number 194 is the smallest for 6 triads"

I presume there are related sequences in the OEIS.

-- Ruud