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 A269701 Cyclic Fibonacci sequence, restricted to maximum=6 1
 0, 1, 1, 2, 3, 5, 2, 1, 3, 4, 1, 5, 6, 5, 5, 4, 3, 1, 4, 5, 3, 2, 5, 1, 6, 1, 1, 2, 3, 5, 2, 1, 3, 4, 1, 5, 6, 5, 5, 4, 3, 1, 4, 5, 3, 2, 5, 1, 6, 1, 1, 2, 3, 5, 2, 1, 3, 4, 1, 5, 6, 5, 5, 4, 3, 1, 4, 5, 3, 2, 5, 1, 6, 1, 1, 2, 3, 5, 2, 1, 3, 4, 1, 5, 6, 5, 5, 4, 3, 1, 4, 5, 3, 2, 5, 1, 6, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Sequence has a period of 24. LINKS Table of n, a(n) for n=0..97. Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1). FORMULA F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1 and F(n) = F(n-1) + F(n-2) - 6 if F(n-1) + F(n-2) > 6. G.f.: ( -x *(1 +x +2*x^2 +3*x^3 +5*x^4 +2*x^5 +x^6 +3*x^7 +4*x^8 +x^9 +5*x^10 +6*x^11 +5*x^12 +5*x^13 +4*x^14 +3*x^15 +x^16 +4*x^17 +5*x^18 +3*x^19 +2*x^20 +5*x^21 +x^22 +6*x^23) ) / ( (x-1) *(1+x+x^2) *(1+x) *(1-x+x^2) *(1+x^2) *(x^4-x^2+1) *(1+x^4) *(x^8-x^4+1) ). - R. J. Mathar, Apr 16 2016 EXAMPLE For n = 6; F(5) + F(4) equals 8 then F(6) = 8 - 6 = 2. MAPLE A269701 := proc(n) option remember; if n <=5 then combinat[fibonacci](n) ; else a := procname(n-1)+procname(n-2) ; if a > 6 then a-6; else a; end if; end if; end proc: # R. J. Mathar, Apr 16 2016 MATHEMATICA Table[Mod[Fibonacci[n], 6], {n, 100}] /. 0 -> 6 (* Alonso del Arte, Mar 28 2016 *) PadRight[{0}, 120, {6, 1, 1, 2, 3, 5, 2, 1, 3, 4, 1, 5, 6, 5, 5, 4, 3, 1, 4, 5, 3, 2, 5, 1}] (* Harvey P. Dale, May 13 2019 *) PROG (Erlang) fibocy(1) -> 1; fibocy(2) -> 1; fibocy(N) when N > 1 -> Tmp = fibocy(N-1) + fibocy(N-2), if Tmp > 6 -> Tmp - 6; true -> Tmp end. CROSSREFS Cf. A000045 (Fibonacci numbers), A082117. Sequence in context: A369060 A369686 A082117 * A011157 A205387 A365424 Adjacent sequences: A269698 A269699 A269700 * A269702 A269703 A269704 KEYWORD nonn,easy,less AUTHOR Gabriel Osorio, Mar 04 2016 STATUS approved

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Last modified September 16 18:59 EDT 2024. Contains 375977 sequences. (Running on oeis4.)