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%I #24 Jan 21 2024 03:21:25
%S 1,1,-1,-5,-35,-1315,-1733045,-3003450166025,
%T -9020712899804610407871655,
%U -81373261220701303171562403760549780420204382316935
%N a(n) = 2*a(n-1) - a(n-2) - (a(n-1)^2 + a(n-2)^2).
%H G. C. Greubel, <a href="/A122590/b122590.txt">Table of n, a(n) for n = 1..14</a>
%F a(n) = 2*a(n-1) - a(n-2) - (a(n-1)^2 + a(n-2)^2), with a(1) = a(2) = 1.
%t a[n_]:= a[n]= If[n<3, 1, 2*a[n-1] -a[n-2] -(a[n-1]^2 +a[n-2]^2)];
%t Table[a[n], {n, 0, 10}]
%t nxt[{a_, b_}] := {b, 2 b - a - (b^2 + a^2)}; NestList[nxt,{1,1},10][[All,1]] (* _Harvey P. Dale_, Aug 15 2021 *)
%o (Magma)
%o function a(n) // a = A122590
%o if n lt 3 then return 1;
%o else return 2*a(n-1) -a(n-2) -(a(n-1)^2 +a(n-2)^2);
%o end if; return a;
%o end function;
%o [a(n): n in [1..12]]; // _G. C. Greubel_, Nov 29 2021
%o (Sage) #a = A122590
%o def a(n): return 1 if (n<3) else 2*a(n-1) -a(n-2) -(a(n-1)^2 +a(n-2)^2)
%o [a(n) for n in (1..12)] # _G. C. Greubel_, Nov 29 2021
%Y Cf. A122591, A122592, A122593.
%K sign
%O 1,4
%A _Roger L. Bagula_, Sep 19 2006
%E Edited by _N. J. A. Sloane_, Sep 21 2006
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