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A079344 F(n) mod 8, where F(n) = A000045(n) is the n-th Fibonacci number. 9
0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5, 2, 7, 1, 0, 1, 1, 2, 3, 5, 0, 5, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

P. Ribenboim, FFF (Favorite Fibonacci Flowers), Fib. Q. 43 (No. 1, 2005), 3-14.

Eric Weisstein's World of Mathematics, Fibonacci Number

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, -1, 1, 0, 0, -1, 1).

FORMULA

Sequence is periodic with Pisano period 12 = A001175(8).

a(n) = (1/396)*{-17*(n mod 12)+49*[(n+1) mod 12]+214*[(n+2) mod 12]-149*[(n+3) mod 12]+115*[(n+4) mod 12]+16*[(n+5) mod 12]-149*[(n+6) mod 12]+181*[(n+7) mod 12]-50*[(n+8) mod 12]-17*[(n+9) mod 12]-17*[(n+10) mod 12]+16*[(n+11) mod 12]} with n>=0. - Paolo P. Lava, Nov 24 2006

a(n) = (1/396)*{49*[n mod 12] + 214*[(n + 1) mod 12] - 149*[(n + 2) mod 12] + 115*[(n + 3) mod 12] + 16*[(n + 4) mod 12] - 149*[(n + 5) mod 12] + 181*[(n + 6) mod 12] - 50*[(n + 7) mod 12] - 17*[(n + 8) mod 12] - 17*[(n + 9) mod 12] + 16*[(n + 10) mod 12] - 17*[(n + 11) mod 12]}, with n>= 0. - Paolo P. Lava, May 30 2007

G.f. -x*(1+x^2+x^3+3*x^4+6*x^6-5*x^5+x^7) / ( (x-1)*(x^2-x+1)*(1+x+x^2)*(x^4-x^2+1) ). - R. J. Mathar, Aug 08 2012

EXAMPLE

a(8) = F(8) mod 8 = 21 mod 8 = 5.

MATHEMATICA

a={}; Do[f=Fibonacci[n]; AppendTo[a, Mod[f, 8]], {n, 1, 30}]; a (* Vladimir Joseph Stephan Orlovsky, Jul 23 2008 *)

Mod[Fibonacci[Range[0, 110]], 8] (* or *) LinearRecurrence[ {1, 0, 0, -1, 1, 0, 0, -1, 1}, {0, 1, 1, 2, 3, 5, 0, 5, 5}, 110] (* Harvey P. Dale, Jan 16 2014 *)

PROG

(PARI) for (n=0, 100, print1(fibonacci(n)%8", "))

(MAGMA) [Fibonacci(n) mod 8: n in [0..100]]; // Vincenzo Librandi, Feb 04 2014

CROSSREFS

Cf. A000045, A011655, A082115, A079343, A082116, A082117, A079344, A079345, A111958.

Sequence in context: A039705 A254271 A082118 * A096535 A126047 A023049

Adjacent sequences:  A079341 A079342 A079343 * A079345 A079346 A079347

KEYWORD

nonn,easy

AUTHOR

Jon Perry, Jan 04 2003

EXTENSIONS

Edited by N. J. A. Sloane, Dec 06 2008 at the suggestion of R. J. Mathar

STATUS

approved

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Last modified September 26 01:25 EDT 2017. Contains 292500 sequences.