A048271 a(0) = 1, a(n+1) = -3*a(n) mod 11.
1, 8, 9, 6, 4, 10, 3, 2, 5, 7, 1, 8, 9, 6, 4, 10, 3, 2, 5, 7, 1, 8, 9, 6, 4, 10, 3, 2, 5, 7, 1, 8, 9, 6, 4, 10, 3, 2, 5, 7, 1, 8, 9, 6, 4, 10, 3, 2, 5, 7, 1, 8, 9, 6, 4, 10, 3, 2, 5, 7, 1, 8, 9, 6, 4, 10, 3, 2, 5, 7, 1, 8, 9, 6, 4, 10, 3, 2, 5, 7, 1, 8, 9, 6, 4, 10, 3, 2, 5, 7, 1, 8, 9, 6, 4, 10, 3, 2, 5, 7, 1, 8, 9, 6, 4, 10, 3, 2, 5, 7, 1, 8, 9, 6, 4, 10, 3, 2, 5, 7
Offset: 0
Links
- R. M. C. de Souza, H. M. de Oliveira and A. N. Kauffman, Trigonometry in Finite Fields and a new Hartley Transform, in Proceedings of the 1998 IEEE International Symposium on Information Theory. Cambridge: IEEE Press, 1998, page 293.
- Joshua Ide and Marc S. Renault, Power Fibonacci Sequences, Fib. Q. 50(2), 2012, 175-179.
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,-1,1). [_R. J. Mathar_, Apr 20 2010]
Programs
-
Mathematica
NestList[Mod[-3#,11]&,1,120] (* Harvey P. Dale, Jun 15 2021 *)
-
Sage
[power_mod(8,n,11)for n in range(0,120)] # Zerinvary Lajos, Nov 28 2009
Formula
a(n) = 8^n mod 11. - Zerinvary Lajos, Nov 28 2009
From R. J. Mathar, Apr 20 2010: (Start)
a(n) = a(n-1) - a(n-5) + a(n-6).
G.f.: (-1-7*x-x^2+3*x^3+2*x^4-7*x^5) / ( (x-1)*(1+x)*(x^4-x^3+x^2-x+1) ). (End)