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Search: id:A010874
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| A010874 |
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Simple periodic sequence. |
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+0
38
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| 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0, 1, 2, 3, 4, 0
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Complement of A002266, since 5*A002266(n)+a(n)=n. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 01 2007
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FORMULA
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Complex representation: a(n)=(1/5)*(1-r^n)*sum{1<=k<5, k*product{1<=m<5,m<>k, (1-r^(n-m))}} where r=exp(2*pi/5*i) and i=sqrt(-1). G.f.: g(x)=(4x^4+3x^3+2x^2+x)/(1-x^5). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 29 2007
Trigonometric representation: a(n)=(16/5)^2*(sin(n*pi/5))^2*sum{1<=k<5, k*product{1<=m<5,m<>k, (sin((n-m)*pi/5))^2}}. Clearly, the squared terms may be replaced by their absolute values '|.|'. This formula can be easily adapted to represent any periodic sequence. G.f.: also g(x)=x(5x^6-6x^5+1)/((1-x^5)(1-x)^2). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 01 2007
a(n) = n mod 5 - Paolo P. Lava (ppl(AT)spl.at), Jun 08 2007
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CROSSREFS
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Partial sums: A130483. Other related sequences A130481, A130482, A130484, A130485.
Cf. A004526, A002264, A002265, A002266.
Adjacent sequences: A010871 A010872 A010873 this_sequence A010875 A010876 A010877
Sequence in context: A031235 A090141 A049264 this_sequence A125926 A125923 A071513
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KEYWORD
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nonn
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AUTHOR
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njas
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