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
Examples
Sequence is periodic with Pisano period 10. - Corrected by U. Takasi, Dec 27 2009
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).
Programs
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Magma
[Fibonacci(n) mod 11: n in [0..100]]; // Vincenzo Librandi, Feb 04 2014
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Mathematica
Mod[Fibonacci[Range[0, 100]], 11] (* Harvey P. Dale, Jul 27 2012 *)
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PARI
for(n=0,100, print1(fibonacci(n)%11, ", ")) \\ G. C. Greubel, Jan 01 2018
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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
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)
Extensions
Added a(0)=0 from Vincenzo Librandi, Feb 04 2014