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%I #27 Sep 08 2022 08:45:27
%S 2,2,2,7,27,377,71252,725274107,19482315963330427,
%T 1006792136061113006060577048627
%N a(n) = a(n-1)*a(n-2)*a(n-3) - 1 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="/A121258/b121258.txt">Table of n, a(n) for n = 0..14</a> (shortened by _N. J. A. Sloane_, Jan 13 2019)
%F a(n) ~ c^(A058265^n), where c = 1.3319334322065642848267... - _Vaclav Kotesovec_, Jun 15 2019
%t RecurrenceTable[{a[0]==a[1]==a[2]==2, a[n] == a[n-1]*a[n-2]*a[n-3] - 1}, a, {n, 0, 15}] (* _G. C. Greubel_, Jun 07 2019 *)
%t nxt[{a_,b_,c_}]:={b,c,a*b*c-1}; NestList[nxt,{2,2,2},10][[All,1]] (* _Harvey P. Dale_, Jun 25 2020 *)
%o (Magma) I:=[2,2,2]; [n le 3 select I[n] else Self(n-1)*Self(n-2)* Self(n-3)-1: n in [1..12]]; // _Vincenzo Librandi_, Nov 14 2011
%o (PARI) a(n) = if(n<3, 2, a(n-1)*a(n-2)*a(n-3) - 1);
%o vector(12, 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-2)*a(n-3) - 1
%o [a(n) for n in (0..12)] # _G. C. Greubel_, Jun 07 2019
%Y Cf. A007660, A055937.
%K nonn,easy
%O 0,1
%A _Jonathan Vos Post_, Aug 22 2006
%E Data corrected by _Vincenzo Librandi_, Nov 14 2011
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