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A010876
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a(n) = n mod 7.
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35
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0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..87.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,1).
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FORMULA
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Complex representation: a(n) = (1/7)*(1-r^n) * Sum_{1<=k<7} k * Product_{1<=m<7, m<>k} (1-r^(n-m)) where r=exp(2*pi/7*i) and i=sqrt(-1).
Trigonometric representation: a(n) = (64/7)^2*(sin(n*pi/7))^2*Sum_{1<=k<7} k*Product_{1<=m<7,m<>k} sin((n-m)*pi/7)^2.
G.f.: ( Sum_{1<=k<7} k*x^k ) / (1 - x^7).
G.f.: x*(6*x^7-7*x^6+1)/((1-x^7)*(1-x)^2). - Hieronymus Fischer, May 31 2007
a(n) = floor(41152/3333333*10^(n+1)) mod 10. - Hieronymus Fischer, Jan 03 2013
a(n) = floor(7625/274514*7^(n+1)) mod 7. - Hieronymus Fischer, Jan 04 2013
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PROG
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(Sage) [power_mod(n, 7, 7) for n in range(0, 81)] # Zerinvary Lajos, Nov 07 2009
(PARI) a(n)=n%7 \\ Charles R Greathouse IV, Dec 05 2011
(Magma) &cat [[0..6]^^20]; // Bruno Berselli, Jun 09 2016
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CROSSREFS
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Partial sums: A130485.
Other related sequences: A130481, A130482, A130483, A130484.
Sequence in context: A037885 A347729 A031007 * A309958 A055400 A257847
Adjacent sequences: A010873 A010874 A010875 * A010877 A010878 A010879
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Formula section re-edited for better readability by Hieronymus Fischer, Dec 05 2011
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STATUS
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approved
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