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A082115
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Fibonacci sequence (mod 3).
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9
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1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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LINKS
| Eric Weisstein's World of Mathematics, Fibonacci Number
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FORMULA
| Sequence is periodic with Pisano period 8.
a(n)=(1/224)*{-19*(n mod 8)+37*[(n+1) mod 8]+37*[(n+2) mod 8]+9*[(n+3) mod 8]-47*[(n+4) mod 8]+65*[(n+5) mod 8]-19*[(n+6) mod 8]+9*[(n+7) mod 8]} - Paolo P. Lava (paoloplava(AT)gmail.com), Nov 21 2006
a(n)=1-floor(n/8)+floor((n-1)/8)+floor((n-3)/8)-2*floor((n-4)/8)+2*floo= r((n-5)/8)-floor((n-7)/8). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 01 2007
a(n)=1+((n mod 8)+((n+1)mod 8)-2*((n+3)mod 8)+2*((n+4)mod = 8)-((n+5)mod 8)-((n+7)mod 8))/8. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 01 2007
G.f.: g(x)=(x+x^2+2x^3+2x^5+2x^6+x^7)/(1-x^8) - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 01 2007
a(n)=A131295(n) mod 3 (for n>0). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 01 2007
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MATHEMATICA
| f[n_]:=Mod[Fibonacci[n], 3]; lst={}; Do[AppendTo[lst, f[n]], {n, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 18 2010]
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CROSSREFS
| Cf. A011655, A082115, A079343, A082116, A082117, A079344, A079344.
Sequence in context: A138231 A155100 A076880 * A161553 A099751 A159937
Adjacent sequences: A082112 A082113 A082114 * A082116 A082117 A082118
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com), Apr 03, 2003
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