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Search: id:A000007
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| A000007 |
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The characteristic function of 0: a(n) = 0^n.
(Formerly M0002)
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+0
151
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| 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, 0
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Changing the offset to 1 gives the arithmetical function a(1)=1, a(n)=0 for n>1, the identity function for Dirichlet multiplication (see Apostol).
Hankel transform (see A001906 for definition) of : A000007 (powers of 0), A000012 (powers of 1), A000079 (powers of 2), A000244 (powers of 3), A000302 (powers of 4), A000351 (powers of 5), A000400 (powers of 6), A000420 (powers of 7), A001018 (powers of 8), A001019 (powers of 9), A011557 (powers of 10), A001020 (powers of 11),etc. ... - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jul 07 2005
This is the identity sequence with respect to convolution. - David W. Wilson (davidwwilson(AT)comcast.net), Oct 30 2006
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REFERENCES
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T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 30.
Paul Barry, A Catalan Transform and Related Transformations on Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.
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LINKS
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David Wasserman, Table of n, a(n) for n = 0..1000
Daniele A. Gewurz and Francesca Merola, Sequences realized as Parker vectors ..., J. Integer Seqs., Vol. 6, 2003.
Index entries for "core" sequences
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FORMULA
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Multiplicative with a(p^e) = 0. - David W. Wilson, Sep 01, 2001
a(n)= floor(1/(n+1)). - Franz Vrabec (franz.vrabec(AT)planetuniqa.at), Aug 24 2005
a(n)=((n+1)!^2 mod (n+2))*((n+2)!^2 mod (n+3)), with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Apr 24 2007
a(n)=1-{[(n+1)!+1] mod (n+1)}, with n>=0. - Paolo P. Lava (ppl(AT)spl.at), May 22 2007
a(n)=1-[(n+2) mod (n+1)], with n>=0. - Paolo P. Lava (ppl(AT)spl.at), Jun 27 2007
a(n)=C(2*n,n) mod 2 - Paolo P. Lava (ppl(AT)spl.at), Aug 31 2007
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MAPLE
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A000007 := proc(n) if n = 0 then 1 else 0; fi; end;
with(combstruct); spec := [A, {A=Z} ]; [seq(combstruct[count](spec, size=n), n=1..20)];
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MATHEMATICA
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a[n_] := If[n == 0, 1, 0]
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PROGRAM
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(PARI) a(n)=!n; for(n=0, 100, print1(a(n)", "))
(MAGMA) [1] cat [0:n in [1..100]]; - from Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006
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CROSSREFS
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Cf. A063524.
Adjacent sequences: A000004 A000005 A000006 this_sequence A000008 A000009 A000010
Sequence in context: A062157 A112347 A134824 this_sequence A014041 A015868 A015824
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KEYWORD
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core,easy,nonn,mult
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AUTHOR
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njas
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