A111958 Lucas numbers (A000032) mod 8.

2, 1, 3, 4, 7, 3, 2, 5, 7, 4, 3, 7, 2, 1, 3, 4, 7, 3, 2, 5, 7, 4, 3, 7, 2, 1, 3, 4, 7, 3, 2, 5, 7, 4, 3, 7, 2, 1, 3, 4, 7, 3, 2, 5, 7, 4, 3, 7, 2, 1, 3, 4, 7, 3, 2, 5, 7, 4, 3, 7, 2, 1, 3, 4, 7, 3, 2, 5, 7, 4, 3, 7, 2, 1, 3, 4, 7, 3, 2, 5, 7, 4, 3, 7, 2, 1, 3, 4, 7, 3, 2, 5, 7, 4, 3, 7, 2, 1, 3, 4, 7, 3, 2, 5, 7

Offset: 0

Author

N. J. A. Sloane, Nov 28 2005

Keywords

• nonn

Comments

This sequence has period-length 12.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..9999
• Paulo Ribenboim, FFF (Favorite Fibonacci Flowers), Fib. Quart. 43 (No. 1, 2005), 3-14.
• Index entries for linear recurrences with constant coefficients, signature (1,-1,1,-1,1,-1,1,-1,1,-1,1).

Crossrefs

Cf. A000032, A079344, A130893.

Programs

Mathematica

LinearRecurrence[{1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1}, {2, 1, 3, 4, 7, 3, 2, 5, 7, 4, 3}, 105] (* Ray Chandler, Aug 27 2015 *)
Mod[LucasL[Range[0, 99]], 8] (* Alonso del Arte, Dec 19 2015 *)

Formula

From G. C. Greubel, Feb 08 2016: (Start)

a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) - a(n-6) + a(n-7) - a(n-8) + a(n-9) - a(n-10) + a(n-11).

a(n+12) = a(n). (End)