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A158068
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Period length 6: repeat 1, 2, 2, 1, 5, 5.
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3
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1, 2, 2, 1, 5, 5, 1, 2, 2, 1, 5, 5, 1, 2, 2, 1, 5, 5, 1, 2, 2, 1, 5, 5, 1, 2, 2, 1, 5, 5, 1, 2, 2, 1, 5, 5, 1, 2, 2, 1, 5, 5, 1, 2, 2, 1, 5, 5, 1, 2, 2, 1, 5, 5, 1, 2, 2, 1, 5, 5, 1, 2, 2, 1, 5, 5, 1, 2, 2, 1, 5, 5, 1, 2, 2, 1, 5, 5, 1, 2, 2, 1, 5, 5, 1, 2, 2, 1, 5, 5, 1, 2, 2, 1, 5, 5, 1, 2, 2, 1, 5, 5, 1, 2, 2
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OFFSET
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0,2
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COMMENTS
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The sequence can be generated starting an array T(n,k) by placing the
periodic sequence 1,2,5 (repeat 1,2,5) in the top row n=0, then defining
the next rows by T(n+1,k) = T(n,k)*T(n,k+1) mod 9, which all have a period T(n,k)=T(n,k+3).
One finds the periodicity T(n+6,k)=T(n,k), and then defines a(n)=T(n,1).
Also the partial fraction expansion of (85+sqrt(12469))/138.
Also the decimal expansion of 11105/90909.
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LINKS
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Table of n, a(n) for n=0..104.
Index to sequences with linear recurrences with constant coefficients, signature (1,-1,1,-1,1).
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FORMULA
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a(n)= a(n-1) -a(n-2) +a(n-3) -a(n-4) +a(n-5).
G.f.: (1+x+5*x^4+x^2)/((1-x)*(1-x+x^2)*(1+x+x^2)) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009]
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EXAMPLE
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a(n)=(1/90)*{76*(n mod 6)+16*[(n+1) mod 6]-44*[(n+2) mod 6]+31*[(n+3) mod 6]+16*[(n+4) mod 6]+[(n+5) mod 6]}, with n>=0 [From Paolo P. Lava, Mar 17 2009]
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CROSSREFS
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Cf. A157742, A158012.
Sequence in context: A099605 A079218 A079220 * A210879 A176265 A187307
Adjacent sequences: A158065 A158066 A158067 * A158069 A158070 A158071
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KEYWORD
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nonn,easy
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AUTHOR
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Paul Curtz, Mar 12 2009
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EXTENSIONS
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Offset set to 0 - R. J. Mathar, Sep 17 2009
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STATUS
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approved
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