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Search: id:A117983
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| A117983 |
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A modified Legendre-binomial transform of 2^n for p=3. |
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+0
1
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| 1, 2, 13, 26, 52, 338, 757, 1514, 9841, 19682, 39364, 255866, 511732, 1023464, 6652516, 14899274, 29798548, 193690562, 387440173, 774880346, 5036722249, 10073444498, 20146888996, 130954778474, 293292210961, 586584421922
(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)/2=a(3n+2)/13; 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)=3^9-1 are a(0),a(1),a(2),a(3),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)*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: A018628 A018657 A018745 this_sequence A018400 A091052 A031090
Adjacent sequences: A117980 A117981 A117982 this_sequence A117984 A117985 A117986
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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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