[seqfan] Re: Interesting sequence

[Arie Groeneveld]

It looks like it is: 2 * A073359.



Op 22-11-16 om 02:39 schreef David Wilson:
> Starting with integer n,  multiply by ((n+1)/n), take the floor, multiply by
> (n/(n-1), take the floor, all the way down to 2/1, call the result f(n).
>
> For example, starting with n = 5
>
> floor(5*(6/5)) = 6,
> floor(6*(5/4)) = 7,
> floor(7*(4/3)) = 9,
> floor(9*(3/2)) = 13,
> floor(14*(2/1)) = 26.
>
> so f(5) = 26.
>
> Starting at n = 1, we have
>
> f = (2, 6,  12, 18, 26, 38, 48, 62, 78, 90, ...)
>
> It's trivial that all elements are even, given the final multiplier 2/1.
>
> It looks to me as if f(n) ~ pi*n^2/4, but I couldn't begin to prove this.
>
>
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