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A076839 a(1) = a(2) = 1; a(n) = (a(n-1)+1)/a(n-2) (for n>2). 7
1, 1, 2, 3, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Any sequence a(1),a(2),a(3),... defined by the recurrence a(n) = (a(n-1)+1)/a(n-2) (for n>2) has period 5. The theory of cluster algebras currently being developed by Fomin and Zelevinsky gives a context for these facts, but it doesn't really explain them in an elementary way. - James Propp, Nov 20 2002

Terms of the simple continued fraction of 34/[sqrt(2405)-29]. Decimal expansion of 1248/11111. - Paolo P. Lava, Aug 05 2009

LINKS

Table of n, a(n) for n=1..105.

Sergey Fomin and Andrei Zelevinsky, Cluster algebras II: Finite type classification

S. Morier-Genoud, V. Ovsienko and S. Tabachnikov, 2-frieze patterns and the cluster structure of the space of polygons, arXiv:1008.3359 [math.AG]

S. Morier-Genoud, V. Ovsienko and S. Tabachnikov, 2-frieze patterns and the cluster structure of the space of polygons, Annales de l'institut Fourier, 62 no. 3 (2012), 937-987. - From N. J. A. Sloane, Dec 26 2012

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 1).

FORMULA

Periodic with period 5.

a(n) = (1/50)*{19*(n mod 5)+19*[(n+1) mod 5]-[(n+2) mod 5]-[(n+3) mod 5]+9*[(n+4) mod 5]}. - Paolo P. Lava, Nov 27 2006

a(1)=1, a(2)=1, a(3)=2, a(4)=3, a(5)=2, a(n)=a(n-5). - Harvey P. Dale, Jan 17 2013

a(n) = ceiling(2*cos(2*Pi*(n+1)/5)+1) + floor(((n+2) mod 5)/3). - Gary Detlefs, May 12 2014

MAPLE

a := 1; b := 1; f := proc(n) option remember; global a, b; if n=1 then a elif n=2 then b else (f(n-1)+1)/f(n-2); fi; end;

MATHEMATICA

RecurrenceTable[{a[1]==a[2]==1, a[n]==(a[n-1]+1)/a[n-2]}, a, {n, 110}] (* or *) LinearRecurrence[{0, 0, 0, 0, 1}, {1, 1, 2, 3, 2}, 110] (* Harvey P. Dale, Jan 17 2013 *)

PROG

(MAGMA) [n le 2 select 1 else  (Self(n-1) + 1) div Self(n-2): n in [1..100]] ; // Vincenzo Librandi, May 23 2019

CROSSREFS

Cf. A076840, A076841, A076844, A076823.

Sequence in context: A306239 A159455 A105734 * A092542 A321305 A026552

Adjacent sequences:  A076836 A076837 A076838 * A076840 A076841 A076842

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Nov 21 2002

STATUS

approved

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Last modified September 17 11:03 EDT 2019. Contains 327129 sequences. (Running on oeis4.)