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%I #16 Apr 08 2014 06:07:07
%S 1,1,1,9,9,75,225,1225,1225,19845,99225,160083,480249,1288287,3006003,
%T 41409225,41409225,1329696225,11967266025,10667118605,53335593025,
%U 85530896451,940839860961,1371086188563,4113258565689,21972535073125,285642955950625,176021737014375
%N Denominator of 2n/v(n)^2, where v(1) = 0, v(2) = 1, and v(n) = v(n-1)/(n-2) + v(n-2) for n >= 3. (Limit of 2n/v(n)^2 is Pi.)
%C Pi = limit of A239224(n)/A239225(n), attributed to B. Cloitre in Finch.
%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, page 19.
%H Clark Kimberling, <a href="/A239225/b239225.txt">Table of n, a(n) for n = 1..1000</a>
%e Let w(n) = 2n/v(n)^2. The first 7 values of w are 4, 6, 32/9, 40/9, 256/75, 896/225, 4096/1225, with approximations 4., 6., 3.55556, 4.44444, 3.41333, 3.98222, 3.34367; w(1000) = 3.14316..., w(10000) = 3.14175..., w(20000) = 3.14167... .
%p v:= proc(n) v(n):= `if`(n<3, n-1, v(n-1)/(n-2)+v(n-2)) end:
%p a:= n-> denom(2*n/v(n)^2):
%p seq(a(n), n=2..30); # _Alois P. Heinz_, Mar 12 2014
%t z = 40; v[1] = 0; v[2] = 1; v[n_] := v[n] = v[n - 1]/(n - 2) + v[n - 2]
%t u = Join[{1}, Table[2 n/v[n]^2, {n, 2, z}]];
%t t1 = Numerator[u] (* A239224 *)
%t t2 = Denominator[u] (* A239225 *)
%Y Cf. A000796, A239224.
%K nonn,frac,easy
%O 1,4
%A _Clark Kimberling_, Mar 12 2014
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