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A076839
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a(1) = a(2) = 1; a(n) = (a(n-1)+1)/a(n-2) (for n>2).
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4
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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; internal format)
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OFFSET
| 1,3
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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. [From Paolo P. Lava (paoloplava(AT)gmail.com), Aug 05 2009]
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LINKS
| Sergey Fomin and Andrei Zelevinsky, Cluster algebras II: Finite type classification
Index to sequences with linear recurrences with constant coefficients, signature (0,0,0,0,1).
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FORMULA
| 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 (paoloplava(AT)gmail.com), Nov 27 2006
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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;
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CROSSREFS
| Cf. A076840, A076841, A076844, A076823.
Sequence in context: A083279 A159455 A105734 * A092542 A026552 A176270
Adjacent sequences: A076836 A076837 A076838 * A076840 A076841 A076842
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 21 2002
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