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Search: id:A006888
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| A006888 |
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a(n) = a(n-1) + a(n-2) a(n-3).
(Formerly M0733)
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+0
3
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| 1, 1, 1, 2, 3, 5, 11, 26, 81, 367, 2473, 32200, 939791, 80570391, 30341840591, 75749670168872, 2444729709746709953, 2298386861814452020993305, 185187471463742319884263934176321
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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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
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
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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
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MATHEMATICA
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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]
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CROSSREFS
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Sequence in context: A027763 A060696 A000628 this_sequence A009589 A098179 A055228
Adjacent sequences: A006885 A006886 A006887 this_sequence A006889 A006890 A006891
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KEYWORD
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nonn,easy
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AUTHOR
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mrob(AT)mrob.com (Robert P Munafo)
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EXTENSIONS
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More terms from Michel ten Voorde (seqfan(AT)tenvoorde.org) Apr 11 2001
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