[seqfan] Interesting sequence
David Wilson
davidwwilson at comcast.net
Tue Nov 22 02:39:50 CET 2016
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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