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A154811
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Fibonacci(2n+1) mod 9.
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9
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1, 2, 5, 4, 7, 8, 8, 7, 4, 5, 2, 1, 1, 2, 5, 4, 7, 8, 8, 7, 4, 5, 2, 1, 1, 2, 5, 4, 7, 8, 8, 7, 4, 5, 2, 1, 1, 2, 5, 4, 7, 8, 8, 7, 4, 5, 2, 1, 1, 2, 5, 4, 7, 8, 8, 7, 4, 5, 2, 1, 1, 2, 5, 4, 7, 8, 8, 7, 4, 5, 2, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Periodic with period length 12. The period 1, 2, 5, 4, 7, 8, 8, 7, 4, 5, 2, 1 is the palindrom of the one in A153990.
There is some connection to A014217 using the formula with phi=(1+sqrt(5))/2 in A001519.
Terms of the simple continued fraction of 4343150/(sqrt(21657897254981)-1671809). [From Paolo P. Lava (paoloplava(AT)gmail.com), Feb 17 2009]
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,0,0,0,0,-1,1).
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FORMULA
| a(n)= A001519(n+1) mod 9 = A122367(n) mod 9 = |A099496(n)| mod 9.
a(n)=(1/132)*{9*(n mod 12)+20*[(n+1) mod 12]+42*[(n+2) mod 12]-2*[(n+3) mod 12]+42*[(n+4) mod 12]+20*[(n+5) mod 12]+9*[(n+6) mod 12]-2*[(n+7) mod 12]-24*[(n+8) mod 12]+20*[(n+9) mod 12]-24*[(n+10) mod 12]-2*[(n+11) mod 12]}, with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Jan 16 2009]
a(n)=a(n-1)-a(n-6)+a(n-7). G.f.: -(1+x+3*x^2-x^3+3*x^4+x^5+x^6)/((x-1)*(x^2+1)*(x^4-x^2+1)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 10 2009]
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PROG
| (PARI) a(n)=fibonacci(n%12*2+1)%9 \\ Charles R Greathouse IV, Dec 21 2011
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CROSSREFS
| Sequence in context: A085801 A023843 A153990 * A036237 A015948 A119733
Adjacent sequences: A154808 A154809 A154810 * A154812 A154813 A154814
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KEYWORD
| nonn,easy
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Jan 15 2009
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EXTENSIONS
| Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 23 2009
Corrected typo in A-number in first formula R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 23 2009
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