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%I #26 Sep 08 2022 08:45:17
%S 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,
%T 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,
%U 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
%N a(n) = Fibonacci(n) mod 11.
%H Vincenzo Librandi, <a href="/A105955/b105955.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,1).
%F From _Colin Barker_, Jan 02 2018: (Start)
%F 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)).
%F a(n) = 38*a(n-7) - a(n-14) for n>9.
%F (End)
%e Sequence is periodic with Pisano period 10. - Corrected by U. Takasi, Dec 27 2009
%t Mod[Fibonacci[Range[0, 100]], 11] (* _Harvey P. Dale_, Jul 27 2012 *)
%o (Magma) [Fibonacci(n) mod 11: n in [0..100]]; // _Vincenzo Librandi_, Feb 04 2014
%o (PARI) for(n=0,100, print1(fibonacci(n)%11, ", ")) \\ _G. C. Greubel_, Jan 01 2018
%o (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
%K nonn,easy
%O 0,4
%A _Shyam Sunder Gupta_, May 05 2005
%E Added a(0)=0 from _Vincenzo Librandi_, Feb 04 2014
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