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A269701 Cyclic Fibonacci sequence, restricted to maximum=6.

%I A269701 #15 Jun 02 2025 12:16:46
%S A269701 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,
%T A269701 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,
%U A269701 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
%N A269701 Cyclic Fibonacci sequence, restricted to maximum=6.
%C A269701 Sequence has a period of 24.
%H A269701 <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, 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).
%F A269701 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.
%F A269701 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
%e A269701 For n = 6; F(5) + F(4) equals 8 then F(6) = 8 - 6 = 2.
%p A269701 A269701 := proc(n)
%p A269701     option remember;
%p A269701     if n <=5 then
%p A269701         combinat[fibonacci](n) ;
%p A269701     else
%p A269701         a := procname(n-1)+procname(n-2) ;
%p A269701         if a > 6 then
%p A269701             a-6;
%p A269701         else
%p A269701             a;
%p A269701         end if;
%p A269701     end if;
%p A269701 end proc: # _R. J. Mathar_, Apr 16 2016
%t A269701 Table[Mod[Fibonacci[n], 6], {n, 100}] /. 0 -> 6 (* _Alonso del Arte_, Mar 28 2016 *)
%t A269701 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 *)
%o A269701 (Erlang)
%o A269701 fibocy(1) -> 1;
%o A269701 fibocy(2) -> 1;
%o A269701 fibocy(N) when N > 1 ->
%o A269701    Tmp = fibocy(N-1) + fibocy(N-2),
%o A269701    if Tmp > 6 -> Tmp - 6;
%o A269701       true -> Tmp
%o A269701    end.
%Y A269701 Cf. A000045 (Fibonacci numbers), A082117.
%K A269701 nonn,easy,less
%O A269701 0,4
%A A269701 _Gabriel Osorio_, Mar 04 2016