

A105955


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


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, 1, 1, 2, 3, 5, 8, 2, 10, 1, 0
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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(n7)  a(n14) 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: A111301 A247193 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



