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a(n) = a(n-1)*a(n-2) - 1.
1

%I #27 Sep 08 2022 08:44:28

%S 0,1,-1,-2,1,-3,-4,11,-45,-496,22319,-11070225,-247076351776,

%T 2735190806339469599,-675800965841611881515781657825,

%U -1848444588685310753420392017318175868503407962176

%N a(n) = a(n-1)*a(n-2) - 1.

%H John Cerkan, <a href="/A001054/b001054.txt">Table of n, a(n) for n = 0..21</a>

%p a:= proc (n) option remember;

%p if n<2 then n

%p else a(n-1)*a(n-2) - 1

%p end if

%p end proc;

%p seq(a(n), n = 0..15); # _G. C. Greubel_, Sep 20 2019

%t RecurrenceTable[{a[0]==0, a[1]==1, a[n]==a[n-1]*a[n-2] -1}, a, {n, 0, 15}] (* _G. C. Greubel_, Sep 20 2019 *)

%o (PARI) m=15; v=concat([0,1], vector(m-2)); for(n=3, m, v[n]=v[n-1]*v[n-2] -1 ); v \\ _G. C. Greubel_, Sep 20 2019

%o (Magma) I:=[0,1]; [n le 2 select I[n] else Self(n-1)*Self(n-2) -1: n in [1..15]]; // _G. C. Greubel_, Sep 20 2019

%o (Sage)

%o def a(n):

%o if (n<2): return n

%o else: return a(n-1)*a(n-2) -1

%o [a(n) for n in (0..15)] # _G. C. Greubel_, Sep 20 2019

%o (GAP) a:=[0,1];; for n in [3..15] do a[n]:=a[n-1]*a[n-2] -1; od; a; # _G. C. Greubel_, Sep 20 2019

%K easy,sign

%O 0,4

%A _R. K. Guy_