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a(n) = (a(n-1)^2 - a(n-2)^4) * a(n-1) / a(n-2)^2 with a(1) = 1, a(2) = 2.
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%I #23 Dec 07 2023 14:37:16

%S 1,2,6,30,-330,257070,128005692870,23279147893155496537470,

%T 388475314992168993748220639081347493631827670

%N 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 The next term (a(10)) has 90 digits and a(11) has 178 digits. - _Harvey P. Dale_, Feb 23 2023

%H G. C. Greubel, <a href="/A242996/b242996.txt">Table of n, a(n) for n = 1..13</a>

%F abs(a(n)) = A127815(n).

%F a(n+1) = a(n) * A242995(n) for all n>0.

%F 0 = a(n)^2*a(n+2) + a(n+1)*(a(n)^4 - a(n+1)^2) for all n>0.

%t 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 nxt[{a_,b_}]:={b,(b^2-a^4) b/a^2}; NestList[nxt,{1,2},10][[;;,1]] (* _Harvey P. Dale_, Feb 23 2023 *)

%o (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 (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 Cf. A127815, A242995.

%K sign

%O 1,2

%A _Michael Somos_, Aug 17 2014