[seqfan] Re: Interesting sequence
Chris Thompson
cet1 at cam.ac.uk
Tue Nov 22 15:06:52 CET 2016
On Nov 22 2016, David Wilson wrote:
>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.
This reminds me a lot of A000960, discussed briefly here a year ago
[ http://list.seqfan.eu/pipermail/seqfan/2015-November/015706.html ].
In fact it seems that ThisSeries(n) = A000960(n+1)-1. Can anyone provide
a proof?
--
Chris Thompson
Email: cet1 at cam.ac.uk
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