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A121256 a(n) = a(n-1)*a(n-3) - 1, starting with a(0)=a(1)=a(2)=2. 1

%I

%S 2,2,2,3,5,9,26,129,1160,30159,3890510,4512991599,136107313634240,

%T 529526864767147062399,2389750292138943783804215786000,

%U 325262492519671886357848434144628838112639999

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

%C Analog of A055937 a(n) = a(n-1)*a(n-2) - 1. What is the equivalent continued fraction and asymptotic representation, by analogy to A007660 a(n) = a(n-1)*a(n-2) + 1 ?

%H Vincenzo Librandi, <a href="/A121256/b121256.txt">Table of n, a(n) for n = 0..22</a> (shortened by _N. J. A. Sloane_, Jan 13 2019)

%t RecurrenceTable[{a[0]==a[1]==a[2]==2,a[n]==a[n-1]a[n-3]-1},a,{n,20}] (* _Harvey P. Dale_, Sep 02 2016 *)

%o (MAGMA) I:=[2,2,2]; [n le 3 select I[n] else Self(n-1)*Self(n-3)-1: n in [1..20]]; // _Vincenzo Librandi_, Nov 14 2011

%o (PARI) a(n) = if(n<3, 2, a(n-1)*a(n-3) - 1);

%o vector(20, n, n--; a(n)) \\ _G. C. Greubel_, Jun 07 2019

%o (Sage)

%o def a(n):

%o if (n==0 or n==1 or n==2): return 2

%o else: return a(n-1)*a(n-3) -1

%o [a(n) for n in (0..20)] # _G. C. Greubel_, Jun 07 2019

%Y Cf. A007660, A055937.

%K easy,nonn

%O 0,1

%A _Jonathan Vos Post_, Aug 22 2006

%E Corrected and extended by _Vincenzo Librandi_, Nov 14 2011

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Last modified July 25 11:55 EDT 2021. Contains 346289 sequences. (Running on oeis4.)