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Search: id:A076844
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| A076844 |
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a(1) = a(2) = a(3) = 1; a(n) = (a(n-1)+a(n-2)+1)/a(n-3) (for n>3). |
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6
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| 1, 1, 1, 3, 5, 9, 5, 3, 1, 1, 1, 3, 5, 9, 5, 3, 1, 1, 1, 3, 5, 9, 5, 3, 1, 1, 1, 3, 5, 9, 5, 3, 1, 1, 1, 3, 5, 9, 5, 3, 1, 1, 1, 3, 5, 9, 5, 3, 1, 1, 1, 3, 5, 9, 5, 3, 1, 1, 1, 3, 5, 9, 5, 3, 1, 1, 1, 3, 5, 9, 5, 3, 1, 1, 1, 3, 5, 9, 5, 3, 1, 1, 1, 3, 5, 9, 5, 3, 1, 1, 1, 3, 5, 9, 5, 3, 1, 1, 1, 3, 5, 9, 5, 3, 1
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Any sequence a(1),a(2),a(3),... defined by the recurrence a(n) = (a(n-1)+a(n-2)+1)/a(n-3) (for n>3) has period 8. - James Propp, Nov 20, 2002
Terms of the simple continued fraction of 778/[sqrt(2223933)-995]. [From Paolo P. Lava (ppl(AT)spl.at), Aug 06 2009]
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FORMULA
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a(n)=1/8*{3*(n mod 8)+3*[(n+1) mod 8]+5*[(n+2) mod 8]-3*[(n+3) mod 8]-[(n+4) mod 8]-[(n+5) mod 8]+[(n+6) mod 8]+[(n+7) mod 8]} with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Nov 27 2006
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MAPLE
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a := 1; b := 1; c := 1; f := proc(n) option remember; global a, b, c; if n=1 then RETURN(a); fi; if n=2 then RETURN(b); fi; if n=3 then RETURN(c); fi; RETURN((f(n-1)+f(n-2)+1)/f(n-3)); end;
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CROSSREFS
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Cf. A076840, A076841, A076839, A076842, A076843.
Sequence in context: A019739 A101298 A138055 this_sequence A048639 A021282 A016613
Adjacent sequences: A076841 A076842 A076843 this_sequence A076845 A076846 A076847
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 21 2002
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