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Search: id:A117977
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| A117977 |
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Legendre-binomial transform of 3^n for p=3. |
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+0
1
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| 1, 4, 7, 28, 112, 196, 703, 2812, 4921, 19684, 78736, 137788, 551152, 2204608, 3858064, 13837852, 55351408, 96864964, 387400807, 1549603228, 2711805649, 10847222596, 43388890384, 75930558172, 272342767321, 1089371069284
(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)*3^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: A061668 A128386 A123767 this_sequence A030687 A047004 A030689
Adjacent sequences: A117974 A117975 A117976 this_sequence A117978 A117979 A117980
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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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