Finding the Pattern of Triangular Set of Numbers

  • Context: Undergrad 
  • Thread starter Thread starter isthereaspoon
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Discussion Overview

The discussion revolves around identifying patterns in a triangular set of numbers presented by a participant. The focus includes exploring mathematical relationships within the triangular arrangement, with an emphasis on the structure of the columns and potential connections to known sequences.

Discussion Character

  • Exploratory, Mathematical reasoning

Main Points Raised

  • One participant notes that the first column appears to follow the formula (x-1)^8.
  • Another participant references Sloane's OEIS entry A130595 as a potential source for understanding the sequence but expresses difficulty in finding additional patterns.
  • A different participant suggests that the 'hypothenuse' of the triangle may have significance, pointing out specific relationships between the numbers in the first few rows.
  • Some participants acknowledge the complexity of the problem, indicating that finding a clear pattern is challenging.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the patterns present in the triangular set of numbers, and multiple competing views and uncertainties remain regarding the relationships and formulas involved.

Contextual Notes

Participants have not fully resolved the mathematical relationships or provided complete definitions for the terms and patterns discussed, leaving some assumptions unaddressed.

isthereaspoon
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I have encountered such a triangular set of numbers:

1
-8 -7
28 -16 9
-56 -65 -22 -7
70 112 51 4 1

Apart from the obvious first column being (x-1)^8, what can you find for other columns?
 
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thanks, it is simply hard.
 
The 'hypothenuse' seems to play a role in that

1
-8 -7
28 -16 9

-7 - 1 = -8
-7 - 9 = -16

As far as the other numbers go I haven't gotten them yet, but just putting this out there as a possible stepping stone
 

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