A269701 Cyclic Fibonacci sequence, restricted to maximum=6

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

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