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 A076844 a(1) = a(2) = a(3) = 1; a(n) = (a(n-1) + a(n-2) + 1)/a(n-3) (for n>3). 5
 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; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS 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). - Paolo P. Lava, Aug 06 2009 LINKS Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 1). FORMULA 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, Nov 27 2006 MAPLE 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; MATHEMATICA nxt[{a_, b_, c_}]:={b, c, (b+c+1)/a}; Transpose[NestList[nxt, {1, 1, 1}, 110]][[1]] (* or *) PadRight[{}, 110, {1, 1, 1, 3, 5, 9, 5, 3}] (* Harvey P. Dale, Jan 13 2015 *) LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 1}, {1, 1, 1, 3, 5, 9, 5, 3}, 105] (* Ray Chandler, Aug 25 2015 *) CROSSREFS Cf. A076840, A076841, A076839, A076842, A076843. Sequence in context: A189044 A299793 A199612 * A198558 A286566 A286467 Adjacent sequences:  A076841 A076842 A076843 * A076845 A076846 A076847 KEYWORD nonn AUTHOR N. J. A. Sloane, Nov 21 2002 STATUS approved

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Last modified August 20 03:48 EDT 2019. Contains 326139 sequences. (Running on oeis4.)