Gabriel Osorio - cp's OEIS frontend

User: Gabriel Osorio

Gabriel Osorio has authored 2 sequences.

A319667 Palindromes a(n) = (10^n + 1)*(10^(n+1) + 1).

22, 1111, 101101, 10011001, 1000110001, 100001100001, 10000011000001, 1000000110000001, 100000001100000001, 10000000011000000001, 1000000000110000000001, 100000000001100000000001, 10000000000011000000000001, 1000000000000110000000000001

Offset: 0

Gabriel Osorio, Sep 25 2018

			For n = 3: (10^3 + 1)(10^4 + 1) = 1001 * 10001 = 10011001, so a(3) = 10011001.

Colin Barker, Table of n, a(n) for n = 0..450
Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

a:=[22,1111,101101];; for n in [4..20] do a[n]:=111*a[n-1]-1110*a[n-2]+1000*a[n-3]; od; a; # Muniru A Asiru, Sep 26 2018

seq((10^n+1)*(10^(n+1)+1),n=0..20); # Muniru A Asiru, Sep 26 2018

a(n) = (10^n+1)*(10^(n+1)+1) \\ Felix Fröhlich, Sep 25 2018

Vec(11*(2 - 121*x + 200*x^2) / ((1 - x)*(1 - 10*x)*(1 - 100*x)) + O(x^15)) \\ Colin Barker, Sep 25 2018

From Colin Barker, Sep 25 2018: (Start)
G.f.: 11*(2 - 121*x + 200*x^2) / ((1 - x)*(1 - 10*x)*(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n>2.
(End)

More terms from Felix Fröhlich, Sep 25 2018

A269701 Cyclic Fibonacci sequence, restricted to maximum=6.

Original entry on oeis.org

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

Gabriel Osorio, Mar 04 2016

Sequence has a period of 24.

			For n = 6; F(5) + F(4) equals 8 then F(6) = 8 - 6 = 2.

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).

Cf. A000045 (Fibonacci numbers), A082117.

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.

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

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 *)

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

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User: Gabriel Osorio

A319667 Palindromes a(n) = (10^n + 1)*(10^(n+1) + 1).

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A269701 Cyclic Fibonacci sequence, restricted to maximum=6.

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