Find the pattern: 12, 44, 130, 342, 840

  • Context: Undergrad 
  • Thread starter Thread starter beamthegreat
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SUMMARY

The forum discussion centers around identifying the pattern in the numerical sequence: 12, 44, 130, 342, 840, 1976, 4518, 10130, 22396, 48996. Users confirmed that the sequence follows an exponential trend and proposed a polynomial function to describe it. The derived formula for the nth term is given by (n+1)(2^(n+1) - 2 - n). Additionally, MATLAB's cftool was used to fit the data, yielding a function of the form f(x) = a*exp(b*x) with parameters a = 14.61 and b = 0.7462.

PREREQUISITES
  • Understanding of exponential functions and polynomial fitting
  • Familiarity with MATLAB and its cftool for curve fitting
  • Basic knowledge of sequences and series in mathematics
  • Experience with data visualization tools like Excel for plotting graphs
NEXT STEPS
  • Learn how to use MATLAB's cftool for advanced curve fitting techniques
  • Explore polynomial regression methods in Python using libraries like NumPy and SciPy
  • Study the properties of exponential growth and its applications in real-world scenarios
  • Investigate the Encyclopedia of Integer Sequences (OEIS) for more sequence patterns and their properties
USEFUL FOR

Mathematicians, data analysts, and anyone interested in sequence analysis and pattern recognition in numerical data.

  • #31
Double Exp.JPG
It is clearly a double exponential.
 
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  • #32
zoki85 said:
... There's possibility no analytical function that coincides with all terms exactly ...
Example? What is the shortest such sequence?
 
  • #33
Keith_McClary said:
Example? What is the shortest such sequence?
No sequence is determined by giving finite number of terms
 
  • #34
zoki85 said:
No sequence is determined by giving finite number of terms
I thought you were saying that there might be no function that agrees with the given finite number of terms. Of course there are many such functions.
 

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