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A117444
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Periodic {0,1,2,-2,-1}.
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4
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0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1, 0, 1, 2, -2, -1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (-1,-1,-1,-1)
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FORMULA
| G.f.: x(1+3x+x^2)/(1+x+x^2+x^3+x^4)=x(1+2x^2-2x^3-x^4)/(1-x^5).
a(n)=sum{k=0..5, L(k(k^2-n)/5)}/2, where L(j/p) is the Legendre symbol of j and p.
a(n)=sqrt(2+2/sqrt(5))*sin(2*pi*n/5)-sqrt(2-2/sqrt(5))*sin(4*pi*n/5).
a(n)=-(1/5)*{(n mod 5)+[(n+1) mod 5]-4*[(n+2) mod 5]+[(n+3) mod 5]+[(n+4) mod 5]}, with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 11 2007
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CROSSREFS
| Sequence in context: A180424 A092339 A079693 * A015504 A055892 A194527
Adjacent sequences: A117441 A117442 A117443 * A117445 A117446 A117447
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 16 2006
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