Search: id:A006888
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%I A006888 M0733
%S A006888 1,1,1,2,3,5,11,26,81,367,2473,32200,939791,80570391,30341840591,
%T A006888 75749670168872,2444729709746709953,2298386861814452020993305,
%U A006888 185187471463742319884263934176321
%N A006888 a(n) = a(n-1) + a(n-2) a(n-3).
%C A006888 Tends towards something like 1.60119...^(1.3247...^n) where 1.3247... 
               = (1/2+sqrt(23/108))^(1/3)+(1/2-sqrt(23/108))^(1/3) is the smallest 
               Pisot-Vijayaraghavan number A060006. Any four consecutive terms are 
               pairwise coprime. - Henry Bottomley (se16(AT)btinternet.com), Sep 
               25 2002
%D A006888 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%F A006888 Lim n->inf a(n)/(a(n-1)*a(n-5)) = 1 agrees with lim n->inf a(n) = c^(P^n) 
               (c=1.60119..., P=PisotV) since PisotV is real root of x^3-x-1 and 
               thus a root of x^5-x^4-1 because x^5-x^4-1 = (x^3-x-1)*(x^2-x+1) 
               and c^(P^n)/(c^(P^(n-1)*c^(P^(n-5)) = c^(P^(n-5)*(P^5-P^4-1)). - 
               Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Aug 14 2004
%t A006888 a=0;b=0;c=1;lst={a,b,c};Do[d=a*b+c;AppendTo[lst,d];a=b;b=c;c=d,{n,2*4!}];
               lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 13 2009]
%Y A006888 Sequence in context: A027763 A060696 A000628 this_sequence A009589 A098179 
               A055228
%Y A006888 Adjacent sequences: A006885 A006886 A006887 this_sequence A006889 A006890 
               A006891
%K A006888 nonn,easy
%O A006888 0,4
%A A006888 mrob(AT)mrob.com (Robert P Munafo)
%E A006888 More terms from Michel ten Voorde (seqfan(AT)tenvoorde.org) Apr 11 2001

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