Create an Equation for 3 Offspring Rabbits

  • Context: Undergrad 
  • Thread starter Thread starter Dusto
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SUMMARY

The discussion focuses on creating a mathematical equation to model rabbit offspring growth, specifically for three offspring per rabbit instead of one. The Fibonacci sequence, represented as Fn = Fn-1 + Fn-2, is adapted to Xn = X(n-1) + 3*X(n-2) to account for the increased number of offspring. The initial attempts to formulate this equation yielded discrepancies, particularly in the sixth generation, where the correct value should be 40 instead of 38. The participants clarified the equation's structure and confirmed its intended application.

PREREQUISITES
  • Understanding of Fibonacci sequence and its mathematical implications
  • Basic knowledge of recursive equations
  • Familiarity with mathematical notation and terminology
  • Concept of generating functions in combinatorial mathematics
NEXT STEPS
  • Research the derivation of recursive sequences in combinatorial contexts
  • Explore variations of the Fibonacci sequence for different offspring scenarios
  • Learn about generating functions and their applications in population modeling
  • Investigate mathematical modeling techniques for exponential growth patterns
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Mathematicians, students studying combinatorial mathematics, and anyone interested in population dynamics and modeling offspring growth in biological systems.

Dusto
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I know that the Fibonnaci equation, Fn = Fn-1 + Fn-2, allows you to calculate (If you are using rabbits) each rabbit giving offspring to one other pair or rabbits. How does one create an equation for three offspring for each rabbit, instead of one? Instead of 0, 1, 1, 2, 3, 5, 8, 13..you have 0, 1, 1, 4, 7, 19, 38. I've been trying to create a formula that matches this, but I'm not sure if I'm doing more work than I need to. If k represents the number of offspring, the closest I have come up with is Xn = X(n-1) + X(n-2) + k + n with n being the generation number, Xn being the number of rabbits. It works for the first few generations but falls apart eventually.
 
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I am not sure I understand your example with the rabbits.
It looks like you are saying instead of ##X_n = X_{n-1} + X_{n-2}## you are changing the game to ##X_n = X_{n-1} +3 X_{n-2}.## But I am not sure how you generated your example sequence...since that method doesn't give 38.
 
Oh lawdy. You're right! That 6th generation should be 40. Not 38. And yes, that equation was exactly what I was aiming for. Much appreciated!
 

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