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%I #12 Jun 14 2018 20:49:29
%S 0,1,2,4,15,118,3536,834481,5901449514,9849294983780932,
%T 116250234190553238066899615,
%U 2289965696952749203147232235388377288832846,532418097118181120851300401934424857560888078403591714456723409727648
%N a(0)=0, a(1)=1, a(2)=2; for n >= 3, a(n) = 2*a(n-1)*a(n-2) - a(n-3).
%D F. Axel et al., Vibrational modes in a one dimensional "quasi-alloy": the Morse case, J. de Physique, Colloq. C3, Supp. to No. 7, Vol. 47 (Jul 1986), pp. C3-181-C3-186; see Eq. (10).
%H Harry J. Smith, <a href="/A065598/b065598.txt">Table of n, a(n) for n = 0..17</a>
%p A065598 := proc(n) option remember; if n <= 2 then n else 2*A065598(n-1)*A065598(n-2)-A065598(n-3); fi; end;
%t nxt[{a_,b_,c_}]:={b,c,2c*b-a}; NestList[nxt,{0,1,2},12][[All,1]] (* _Harvey P. Dale_, Aug 31 2017 *)
%o (PARI) { for (n = 0, 17, if (n>2, a=2*a1*a2-a3; a3=a2; a2=a1; a1=a, if (n==0, a=a3=0, if (n==1, a=a2=1, a=a1=2))); write("b065598.txt", n, " ", a) ) } \\ _Harry J. Smith_, Oct 23 2009
%Y Cf. A065597.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Dec 01 2001
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