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Search: id:A117976
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| A117976 |
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Legendre-binomial transform of 2^n for p=3. |
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+0
1
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| 1, 3, 3, 9, 27, 27, 57, 171, 171, 513, 1539, 1539, 4617, 13851, 13851, 29241, 87723, 87723, 261633, 784899, 784899, 2354697, 7064091, 7064091, 14913081, 44739243, 44739243, 134217729, 402653187, 402653187, 1207959561
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(3n)=a(3n+1)/a(1)=a(3n+2)/a(2); a(9n)=a(9n+3)/a(3)=a(9n+6)/a(6); a(27n)=a(27n+9)/a(9)=a(27n+18)/a(18); a(3^k*n)=a(3^k*n+3^(k-1))/a(3^(k-1))=a(3^k*n+2*3^(k-1))/a(2*3^(k-1)), k>0.
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FORMULA
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a(n)=sum{k=0..n, L(C(n,k)/3)*2^k} where L(j/p) is the Legendre symbol of j and p.
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CROSSREFS
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Sequence in context: A007683 A059728 A083008 this_sequence A010098 A029857 A032086
Adjacent sequences: A117973 A117974 A117975 this_sequence A117977 A117978 A117979
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Apr 06 2006
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