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a(n) = a(n-1)*a(n-3)+1 with a(0)=a(1)=a(2)=0.
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%I #15 Sep 08 2022 08:45:27

%S 0,0,0,1,1,1,2,3,4,9,28,113,1018,28505,3221066,3279045189,

%T 93469183112446,301070407771273987437,987223472152664180906141290594,

%U 92274971491542102812339702600558728264132925

%N a(n) = a(n-1)*a(n-3)+1 with a(0)=a(1)=a(2)=0.

%C Analog of A007660 a(n)=a(n-1)*a(n-2)+1. What is the equivalent continued fraction and asymptotic representation?

%H Vincenzo Librandi, <a href="/A121253/b121253.txt">Table of n, a(n) for n = 0..26</a> (shortened by _N. J. A. Sloane_, Jan 13 2019)

%t RecurrenceTable[{a[0]==a[1]==a[2]==0,a[n]==a[n-1]a[n-3]+1},a,{n,20}] (* _Harvey P. Dale_, Dec 30 2011 *)

%o (Magma) I:=[0,0,0]; [n le 3 select I[n] else Self(n-1)*Self(n-3)+1: n in [1..20]]; // _Vincenzo Librandi_, Nov 14 2011

%Y Cf. A007660.

%K nonn,easy

%O 0,7

%A _Jonathan Vos Post_, Aug 22 2006

%E More terms from _Vincenzo Librandi_, Nov 14 2011