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Search: id:A154955
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| A154955 |
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1,-1 followed by 0,0,0... |
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+0
1
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| 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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Matrix inverse of A000012.
Moebius transform of a simple periodic sequence (A000035). Dirichlet inverse of A036987(n-1). Partial sums of a(n) is characteristic function of 1 (A063524). a(n)=(-1)^(n+1)*A019590(n). a(n) for n >= 1 is Dirichlet convolution of following functions b(n), c(n), a(n) = Sum_{d|n} b(d)*c(n/d)): a(n) = A000012(n) * A092673(n). Examples of Dirichlet convolutions with function a(n), i.e. b(n) = Sum_{d|n} a(d)*c(n/d): a(n) * A000012(n) = A000035(n), a(n) * A000027(n) = A026741(n), a(n) * A008683(n) = A092673(n), a(n) * A036987(n-1) = A063524(n), a(n) * A000005(n) = A001227(n). [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 21 2009]
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FORMULA
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a(n)={C[2*(n-1),n-1] mod 2}-[C(n^2,n+2) mod 2], with n>=1 [From Paolo P. Lava (ppl(AT)spl.at), Jan 22 2009]
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CROSSREFS
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Cf. A000035, A036987, A063524, A019590, A000012, A000027, A026741, A008683, A092673, A000005, A001227. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Mar 21 2009]
Sequence in context: A134323 A060576 A019590 this_sequence A014040 A014071 A014038
Adjacent sequences: A154952 A154953 A154954 this_sequence A154956 A154957 A154958
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KEYWORD
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sign,tabl
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AUTHOR
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Mats Granvik (mats.granvik(AT)abo.fi), Jan 18 2009
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