Solve 8c Stamp Problem with Recurrence Relation

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SUMMARY

The discussion focuses on solving the 8c Stamp Problem using a recurrence relation. The goal is to determine the number of combinations of 1 cent, 2 cents, and 3 cents stamps that total eight cents, which is established to be 81. The method involves interpreting the coefficient of x^8 in the expansion of the polynomial (x+x^2+x^3)^n, where n represents the number of stamps used. This approach eliminates the need for programming by leveraging combinatorial mathematics.

PREREQUISITES
  • Understanding of recurrence relations
  • Familiarity with polynomial expansions
  • Basic combinatorial mathematics
  • Knowledge of generating functions
NEXT STEPS
  • Study the concept of generating functions in combinatorics
  • Learn how to derive coefficients from polynomial expansions
  • Explore advanced recurrence relations and their applications
  • Investigate combinatorial proofs for counting problems
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Mathematicians, computer scientists, and students interested in combinatorial problem-solving and recurrence relations.

Punkyc7
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Use a recurrence relation to find the number of ways that stamps that have a value of 1 cent , 2 cents and a 3 cents can add up to eight cents.

How exactly do you go about solving a problem like this without writing a program to find all the possibilities?

The answer given is 81, but I have know Idea how to get it.
 
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How would you interpret the coefficient of x^8 in the expansion of (x+x^2+x^3)^n?

RGV
 
Would that be the number of times a certain combination happens?
 

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