cp's OEIS Frontend

A242996 a(n) = (a(n-1)^2 - a(n-2)^4) * a(n-1) / a(n-2)^2 with a(1) = 1, a(2) = 2.

%I A242996 #23 Dec 07 2023 14:37:16
%S A242996 1,2,6,30,-330,257070,128005692870,23279147893155496537470,
%T A242996 388475314992168993748220639081347493631827670
%N A242996 a(n) = (a(n-1)^2 - a(n-2)^4)  * a(n-1) / a(n-2)^2 with a(1) = 1, a(2) = 2.
%C A242996 The next term (a(10)) has 90 digits and a(11) has 178 digits. - _Harvey P. Dale_, Feb 23 2023
%H A242996 G. C. Greubel, <a href="/A242996/b242996.txt">Table of n, a(n) for n = 1..13</a>
%F A242996 abs(a(n)) = A127815(n).
%F A242996 a(n+1) = a(n) * A242995(n) for all n>0.
%F A242996 0 = a(n)^2*a(n+2) + a(n+1)*(a(n)^4 - a(n+1)^2) for all n>0.
%t A242996 RecurrenceTable[{a[n] == (a[n-1]^2 - a[n-2]^4)*a[n-1]/a[n-2]^2, a[1] == 1, a[2] == 2}, a, {n, 1, 10}] (* _G. C. Greubel_, Aug 06 2018; corrected by _Georg Fischer_, Dec 07 2023 *)
%t A242996 nxt[{a_,b_}]:={b,(b^2-a^4) b/a^2}; NestList[nxt,{1,2},10][[;;,1]] (* _Harvey P. Dale_, Feb 23 2023 *)
%o A242996 (PARI) {a(n) = if( n<3, max(0, n), my(x = a(n-2)^2, y = a(n-1)); (y^2 - x^2) * y / x)};
%o A242996 (Magma) I:=[1,2]; [n le 2 select I[n] else (Self(n-1)^2 - Self(n-2)^2 )/Self(n-2)^2: n in [1..10]]; // _G. C. Greubel_, Aug 06 2018
%Y A242996 Cf. A127815, A242995.
%K A242996 sign
%O A242996 1,2
%A A242996 _Michael Somos_, Aug 17 2014