%I #9 Aug 20 2024 16:29:30

%S 0,1,2,7,94,17623,621131422,771608486480914039,

%T 1190759312818733806192492198418844958,

%U 2835815482129086304432303489823255992516794878843873643408264712776750007

%N a(n) = 2*a(n-1)^2 - a(n-2)^2 with a(0)=0, a(1)=1.

%H G. C. Greubel, <a href="/A076740/b076740.txt">Table of n, a(n) for n = 0..12</a>

%e a(2) = 2*1^2 - 0^2 = 2 - 0 = 2.

%e a(3) = 2*2^2 - 1^2 = 8 - 1 = 7.

%e a(4) = 2*7^2 - 2^2 = 98 - 4 = 94.

%t a[n_]:= a[n]= If[n<2, n, 2*a[n-1]^2 - a[n-2]^2 ];

%t Table[a[n], {n, 0, 12}] (* _G. C. Greubel_, May 02 2022 *)

%t nxt[{a_,b_}]:={b,2b^2-a^2}; NestList[nxt,{0,1},10][[;;,1]] (* _Harvey P. Dale_, Aug 20 2024 *)

%o (PARI) a=vector(10); a[1]=0; a[2]=1; for (i=3,10,a[i]=2*a[i-1]^2-a[i-2]^2); a

%o (SageMath)

%o def a(n): # a = A076740

%o if (n<2): return n

%o else: return 2*a(n-1)^2 - a(n-2)^2

%o [a(n) for n in (0..12)] # _G. C. Greubel_, May 02 2022

%K nonn

%O 0,3

%A _Jon Perry_, Jun 19 2003