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%I #19 May 02 2022 01:39:15
%S 0,1,2,6,64,8120,131860608,34774439752390528,
%T 2418523320185277177863741363978240,
%U 11698510100560033501377640350194228137500049288930688305497138757632
%N a(n) = 2*a(n-1)^2 - 2*a(n-2)^2 with a(0) = 0, a(1) = 1.
%H Harry J. Smith, <a href="/A061999/b061999.txt">Table of n, a(n) for n = 0..12</a>
%F a(n) = A062000(n)/2.
%t Join[{a=0,b=1},Table[c=2*b^2-2*a^2;a=b;b=c,{n,10}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 22 2011 *)
%t nxt[{a_,b_}]:={b,2b^2-2a^2}; NestList[nxt,{0,1},10][[All,1]] (* _Harvey P. Dale_, Apr 05 2022 *)
%o (PARI) { for (n=0, 12, if (n>1, a=2*a1^2-2*a2^2; a2=a1; a1=a, if (n==0, a=a2=0, a=a1=1)); write("b061999.txt", n, " ", a) ) } \\ _Harry J. Smith_, Jul 29 2009
%o (SageMath)
%o def a(n): # a = A061999
%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..14)] # _G. C. Greubel_, May 01 2022
%Y Cf. A062000.
%K nonn
%O 0,3
%A _Henry Bottomley_, May 29 2001
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