- #31
Laszlogm
- 1
- 0
Find the pattern: 12, 44, 130, 342, 840
- Context: Undergrad
- Thread starter beamthegreat
- Start date
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Discussion Overview
The discussion revolves around identifying the pattern in a numerical sequence: 12, 44, 130, 342, 840, and additional terms. Participants explore various mathematical approaches and models to derive a function that fits the sequence, including polynomial and exponential forms.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
- Mathematical reasoning
Main Points Raised
- Some participants express uncertainty about whether a clear pattern exists in the sequence.
- Others assert that the sequence is correct and provide additional terms to support their claims.
- A participant suggests that the sequence may represent population growth from a video game, which could influence the nature of the pattern.
- Several participants propose different mathematical models, including polynomial and exponential functions, to fit the sequence.
- One participant claims to have derived a specific formula for the sequence: (n+1)(2^{n+1}-2-n).
- Another participant discusses the possibility that no analytical function perfectly fits all terms, but rather describes a general trend.
- Some participants engage in discussions about the methods used to derive formulas, including factorization and difference analysis.
- There are mentions of using software tools like MATLAB and WolframAlpha to find polynomial fits, with varying degrees of success.
- One participant notes that the derived formula corresponds to a combinatorial interpretation related to minimal covers of sets.
- Another participant shares a new sequence they created and invites others to discover its formula.
Areas of Agreement / Disagreement
Participants do not reach a consensus on the existence of a clear pattern or the best mathematical model to describe the sequence. Multiple competing views and approaches remain throughout the discussion.
Contextual Notes
Some discussions involve assumptions about the nature of the sequence and the methods used to analyze it, which may not be universally applicable. The reliance on specific software for fitting functions introduces additional complexity and potential limitations.
Who May Find This Useful
This discussion may be useful for individuals interested in numerical sequences, mathematical modeling, and combinatorial interpretations, as well as those looking for collaborative problem-solving approaches in mathematics.
- #32
Keith_McClary
- 752
- 1,506
Example? What is the shortest such sequence?zoki85 said:
- #33
zoki85
- 1,198
- 230
No sequence is determined by giving finite number of termsKeith_McClary said:
- #34
Keith_McClary
- 752
- 1,506
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.zoki85 said:
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