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Denominators of w(n) where w(1)=w(2)=w(3)=1, w(n)=(w(n-1)*w(n-2)+(w(n-1)+w(n-2))/3) / w(n-3).
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%I #18 Apr 04 2022 08:27:41

%S 3,9,3,3,1,3,3,9,3,3,1,3,3,9,3,1,1,1,3,9,3,3,1,3,3,9,3,3,1,3,3,9,3,1,

%T 1,1,3,9,3,3,1,3,3,9,3,3,1,3,3,9,3,1,1,1,3,9,3,3,1,3,3,9,3,3,1,3,3,9,

%U 3,1,1,1,3,9,3,3,1,3,3,9,3,3,1,3,3,9,3,1,1,1,3,9,3,3,1,3,3,9,3,3,1,3,3,9,3

%N Denominators of w(n) where w(1)=w(2)=w(3)=1, w(n)=(w(n-1)*w(n-2)+(w(n-1)+w(n-2))/3) / w(n-3).

%C Sequence contains 1,3 or 9 only and is periodic with period (3,9,3,3,1,3,3,9,3,3,1,3,3,9,3,1,1,1) of length 18.

%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

%e The sequence w() begins: 1, 1, 1, 5/3, 23/9, 17/3, 31/3, 25, 143/3, 353/3, 2039/9, 1685/3, 3251/3, 2689, 15571/3, ...

%t LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},{3, 9, 3, 3, 1, 3, 3, 9, 3, 3, 1, 3, 3, 9, 3, 1, 1, 1},105] (* _Ray Chandler_, Aug 25 2015 *)

%t PadRight[{},120,{3,9,3,3,1,3,3,9,3,3,1,3,3,9,3,1,1,1}] (* _Harvey P. Dale_, Apr 04 2022 *)

%Y Cf. A072561, A072557.

%K nonn,frac

%O 1,1

%A _Benoit Cloitre_, Aug 06 2002