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%I #12 Jun 18 2018 09:01:55
%S 0,1,1,2,3,11,64,1405,179829,505319426,181742174114903,
%T 183675702207469683831527,66763242902534057178758511601478574336,
%U 24525571043541618855545577854946122156632189794267317765667241
%N a(0)=0, a(1)=1, a(2)=1; for n >= 3, a(n) = 2*a(n-1)*a(n-2) - a(n-3).
%H Harry J. Smith, <a href="/A065597/b065597.txt">Table of n, a(n) for n = 0..18</a>
%H F. Axel et al., <a href="https://hal.archives-ouvertes.fr/jpa-00225729">Vibrational modes in a one dimensional "quasi-alloy": the Morse case</a>, J. de Physique, Colloq. C3, Supp. to No. 7, Vol. 47 (Jul 1986), pp. C3-181-C3-186; see Eq. (10).
%p A065597 := proc(n) option remember; if n <= 1 then n else 2*A065597(n-1)*A065597(n-2)-A065597(n-3); fi; end;
%o (PARI) { for (n = 0, 18, 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=1))); write("b065597.txt", n, " ", a) ) } \\ _Harry J. Smith_, Oct 23 2009
%Y Cf. A065598.
%K nonn,easy
%O 0,4
%A _N. J. A. Sloane_, Dec 01 2001