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A010880
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Simple periodic sequence.
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4
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n)=n mod 11. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 30 2007
Complex representation: a(n)=1/11*(1-r^n)*sum{1<=k<11, k*product{1<=m<11,m<>k, (1-r^(n-m))}} where r=exp(2*pi/11*i) and i=sqrt(-1). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 30 2007
Trigonometric representation: a(n)=(1024/11)^2*(sin(n*pi/11))^2*sum{1<=k<11, k*product{1<=m<11,m<>k, (sin((n-m)*pi/11))^2}}. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 30 2007
G.f.: g(x)=(sum{1<=k<11, k*x^k})/(1-x^11). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 30 2007
Also: g(x)=x(10x^11-11x^10+1)/((1-x^11)(1-x)^2). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 30 2007
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PROG
| (Other) sage: [power_mod(n, 11, 11)for n in xrange(0, 78)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 07 2009]
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CROSSREFS
| Partial sums: A130489. Other related sequences A130481, A130482, A130483, A130484, A130485, A130486, A130487, A130488.
Sequence in context: A072139 A122638 A090175 * A097462 A190599 A010889
Adjacent sequences: A010877 A010878 A010879 * A010881 A010882 A010883
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Correction. Typo at the sum formula for the g.f.: the summation index should not read "1<=k<10" but "1<=k<11" (see corrected formula).
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