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A quadratic recursion sequence: a(n)=a(n - 1)^2 - 2*a(n - 1) - a(n - 2)^2 + 2*a(n - 2).
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%I #6 Aug 15 2021 16:35:21

%S 1,2,1,-1,4,5,7,20,325,104615,10943984020,119770786197183303365,

%T 14345041226291394498726932547331126324135,

%U 205780207783999715270619814569860727079365052973702253248437750317796955577133460

%N A quadratic recursion sequence: a(n)=a(n - 1)^2 - 2*a(n - 1) - a(n - 2)^2 + 2*a(n - 2).

%F a(n)=a(n - 1)^2 - 2*a(n - 1) - a(n - 2)^2 + 2*a(n - 2).

%F log a(n) ~ 0.011287... * 2^n - _Charles R Greathouse IV_, Oct 06 2009

%t Clear[a, n]; a[0] = 1; a[1] = 2; a[n_] := a[n] = a[n - 1]^2 - 2*a[n - 1] - a[n - 2]^2 + 2*a[n - 2]; Table[a[n], {n, 0, 15}]

%t nxt[{a_,b_}]:={b,b^2-2b-a^2+2a}; NestList[nxt,{1,2},15][[All,1]] (* _Harvey P. Dale_, Aug 15 2021 *)

%K sign

%O 1,2

%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 23 2008

%E Corrected by _Harvey P. Dale_, Aug 15 2021