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A263047 a(1)=0, a(2)=1, a(3)=2; for n>3, a(n) = a(n-3)*a(n-1) - a(n-2).

%I A263047 #25 Sep 08 2022 08:46:14
%S A263047 0,1,2,-1,-3,-5,8,-19,87,715,-13672,-1190179,-850964313,
%T A263047 11634385277515,-13847001034356560872,11783303722311508585098883421,
%U A263047 137091495347348713307137824784782074139687,-1898306077876225285447341619480271058010077969630158545410485
%N A263047 a(1)=0, a(2)=1, a(3)=2; for n>3, a(n) = a(n-3)*a(n-1) - a(n-2).
%p A263047 a[1]:= 0: a[2]:= 1: a[3]:= 2:
%p A263047 for n from 4 to 20 do
%p A263047   a[n]:= a[n-3]*a[n-1]-a[n-2]
%p A263047 od:
%p A263047 seq(a[i],i=1..20); # _Robert Israel_, Oct 08 2015
%t A263047 nxt[{a_,b_,c_}]:={b,c,a*c-b}; NestList[nxt,{0,1,2},20][[All,1]] (* _Harvey P. Dale_, Feb 02 2022 *)
%o A263047 (PARI) a(n) = if(n<4, n-1, a(n-3)*a(n-1)-a(n-2));
%o A263047 vector(20, n, a(n)) \\ _Altug Alkan_, Oct 08 2015
%o A263047 (Magma) [n le 3 select n-1 else Self(n-3)*Self(n-1)-Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Oct 09 2015
%K A263047 sign
%O A263047 1,3
%A A263047 _Gianmarco Giordano_, Oct 08 2015