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The first three terms are 1. After that, a(n)=(a(n-1))^2-a(n-2)-a(n-3).
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%I #6 Nov 21 2013 12:49:06

%S 1,1,1,-1,-1,1,3,9,77,5917,35010803,1225756326698815,

%T 1502478572442172090395687387505,

%U 2257441860647867366107450759398738024116019978304775668415407

%N The first three terms are 1. After that, a(n)=(a(n-1))^2-a(n-2)-a(n-3).

%e a(9)=9^2-3-1=77.

%t a[n_]:=a[n]=a[n-1]^2-a[n-2]-a[n-3]; a[1]=a[2]=a[3]=1

%t Transpose[NestList[Flatten[{Rest[#],Last[#]^2-Total[Most[#]]}]&,{1,1,1},15]][[1]] (* _Harvey P. Dale_, Apr 28 2012 *)

%K sign

%O 1,7

%A _Ben Branman_, Nov 06 2007, Nov 07 2007