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Search: id:A117984
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| A117984 |
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A modified Legendre-binomial transform of 4^n for p=3. |
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+0
1
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| 1, 3, 21, 63, 189, 1323, 4161, 12483, 87381, 262143, 786429, 5505003, 16515009, 49545027, 346815189, 1090777023, 3272331069, 22906317483, 68719738881, 206159216643, 1443114516501, 4329343549503, 12988030648509, 90916214539563
(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)/3=a(3n+2)/21; 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. Divisors of a(9)=4^9-1 include a(0),a(1),a(2),a(3),a(4),a(6),a(7),a(8),a(9).
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FORMULA
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a(n)=sum{k=0..n, (-1)^(n-k)*L(C(n,k)/3)*4^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: A039595 A033567 A129212 this_sequence A050615 A145658 A083564
Adjacent sequences: A117981 A117982 A117983 this_sequence A117985 A117986 A117987
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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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