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Editorial Team
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Asked: 2026-06-10T17:45:10+00:00

I have been challenged to find the general term or the recurrence relation for

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I have been challenged to find the general term or the recurrence relation for this sequence

5,18,44,96,195….
The only hint I have is that this sequence is an applied Fibonacci sequence.
Can someone please suggest ways to find the recurrence or the nth term.
I have looked at OEIS but found no note this for this particular integer sequence.
I have searched at numerous locations but have had no success.
Also ,I think the terms of this sequence can be determined in logarithmic time.
Any help will be highly appreciated.

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1 Answer

  1. Editorial Team

    A closed form of the sequence is

    a(n) = (n*Luc(n+6) - 4*Fib(n))/5

    where Luc(k) is the k-th Lucas number, and Fib(k) the k-th Fibonacci number. Since Luc(k) = Fib(k+1) + Fib(k-1), the formula can easily be rewritten to use only Fibonacci numbers.

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