[seqfan] Re: Significance of sequence relating powers of two and Fibonacci numbers

[M. F. Hasler]

On Fri, Jul 7, 2023 at 3:46 PM Alonso Del Arte <> wrote:

> a very loose upper bound for the number of numbers in A3714 less than 2^n
> is 2^n itself.

Allocating an array with that upper bound wastes A8466(*n*) array slots.

(...)

0, 3, 11, 30, 73, 167, 368, 791, 1671, 3486, 7205, 14787, 30184,

etc. (...).: 2^n − F(n + 3).
> Does this sequence have any meaningful connection to the binary strings
> problem?
>

As you wrote and one can read there,
oeis.org/A8466 (n) := 2^n - Fibonacci(n+2)
is indeed related to binary words in several ways,
and your sequence  2^n - F(n+3)  is just  A8466(n+1) - 2^n,
where 2^n is half of 2^(n+1) -- so it's related in a very similar way.

- Maximilian


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