A105955 a(n) = Fibonacci(n) mod 11.

0, 1, 1, 2, 3, 5, 8, 2, 10, 1, 0, 1, 1, 2, 3, 5, 8, 2, 10, 1, 0, 1, 1, 2, 3, 5, 8, 2, 10, 1, 0, 1, 1, 2, 3, 5, 8, 2, 10, 1, 0, 1, 1, 2, 3, 5, 8, 2, 10, 1, 0, 1, 1, 2, 3, 5, 8, 2, 10, 1, 0, 1, 1, 2, 3, 5, 8, 2, 10, 1, 0, 1, 1, 2, 3, 5, 8, 2, 10, 1, 0, 1, 1, 2, 3, 5, 8, 2, 10, 1, 0, 1, 1, 2, 3, 5, 8, 2, 10, 1, 0

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,1).

Formula

From Colin Barker, Jan 02 2018: (Start)

G.f.: x*(1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 8*x^5 + 2*x^6 + 10*x^7 + x^8) / ((1 - x)*(1 + x)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)).

a(n) = 38*a(n-7) - a(n-14) for n>9.

(End)

Example

Sequence is periodic with Pisano period 10. - Corrected by U. Takasi, Dec 27 2009

Mathematica

Mod[Fibonacci[Range[0, 100]], 11] (* Harvey P. Dale, Jul 27 2012 *)

Prog

(Magma) [Fibonacci(n) mod 11: n in [0..100]]; // Vincenzo Librandi, Feb 04 2014
(PARI) for(n=0, 100, print1(fibonacci(n)%11, ", ")) \\ G. C. Greubel, Jan 01 2018
(PARI) concat(0, Vec(x*(1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 8*x^5 + 2*x^6 + 10*x^7 + x^8) / ((1 - x)*(1 + x)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)) + O(x^100))) \\ Colin Barker, Jan 02 2018

Crossrefs

Sequence in context: A247193 A362358 A096320 * A003893 A152303 A064737

Adjacent sequences: A105952 A105953 A105954 * A105956 A105957 A105958

Keyword

nonn,easy

Author

Shyam Sunder Gupta, May 05 2005

Extensions

Added a(0)=0 from Vincenzo Librandi, Feb 04 2014

Status

approved