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AlfredFlaßhaar15-Moonstone
15-Moonstone
April 25, 2023
Solved

Programming a recursion

  • April 25, 2023
  • 1 reply
  • 1899 views

A friendly hello to all,
again i need help. It's about the recursion u(n+2)=7*u(n+1)-3*u(n)+3 for natural numbers n. How does the calculation and tabulation work in MC15? In derive I managed it successfully. But in MC15 everything is possible, just not the correct result. I just can't get a grip on programming in MC 😞 .
The background is the transformation of the formula u(n)=((1/2)*(7+sqrt(37))^n+((1/2)*(7-sqrt(37))^n-1 given in Binet-Art into a recursion and examination of divisibility by 3.
Kind regards, Alfred Flasshaar

Best answer by Werner_E

See if the attached file helps.

 

I wonder why you would like to use the recursion when a non-recursive formula is available.

1 reply

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Werner_E25-Diamond I
25-Diamond I
April 25, 2023

What about the initial values u(0) and u(1) ?

 

A
AlfredFlaßhaar15-MoonstoneAuthor
15-Moonstone
April 25, 2023

The Binet formula given here and the recursion are equivalent, which was derived in a different way (characteristic polynomial). Accordingly, u(1)=6 and u(2)=42.

W
Werner_E25-Diamond IAnswer
25-Diamond I
April 25, 2023

See if the attached file helps.

 

I wonder why you would like to use the recursion when a non-recursive formula is available.

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