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A006888 a(n) = a(n-1) + a(n-2) a(n-3).
(Formerly M0733)
3
1, 1, 1, 2, 3, 5, 11, 26, 81, 367, 2473, 32200, 939791, 80570391, 30341840591, 75749670168872, 2444729709746709953, 2298386861814452020993305, 185187471463742319884263934176321 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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, Sep 25 2002

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..30

FORMULA

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, Aug 14 2004

MATHEMATICA

a=1; b=1; c=1; lst={a, b, c}; Do[d=a*b+c; AppendTo[lst, d]; a=b; b=c; c=d, {n, 2*4!}]; lst  (* Vladimir Joseph Stephan Orlovsky, Sep 13 2009 *)

CROSSREFS

Sequence in context: A000628 A273755 A258804 * A009589 A098179 A055228

Adjacent sequences:  A006885 A006886 A006887 * A006889 A006890 A006891

KEYWORD

nonn,easy

AUTHOR

Robert Munafo

EXTENSIONS

More terms from Michel ten Voorde (seqfan(AT)tenvoorde.org) Apr 11 2001

Typo in Mathematica code corrected by Vincenzo Librandi, Jun 09 2013

STATUS

approved

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Last modified September 26 14:12 EDT 2017. Contains 292529 sequences.