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Search: id:A010876
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| A010876 |
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Simple periodic sequence. |
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+0
26
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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
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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a(n)=n mod 7. 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.: g(x)=(sum{1<=k<7, k*x^k})/(1-x^7). Also: g(x)=x(6x^7-7x^6+1)/((1-x^7)(1-x)^2). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 31 2007
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CROSSREFS
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Partial sums: A130485. Other related sequences A130481, A130482, A130483, A130484.
Adjacent sequences: A010873 A010874 A010875 this_sequence A010877 A010878 A010879
Sequence in context: A037849 A037885 A031007 this_sequence A055400 A070553 A080743
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KEYWORD
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nonn
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AUTHOR
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njas
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