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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
200
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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
a(A000004(n)) = 1; a(A000027(n)) = 0. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 12 2008]
(1+(-1)^nth prime)/2. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 25 2009]
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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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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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
Index entries for characteristic functions
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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)aon.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
a(n)=((-1)^A000040(n)+1)/2. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 25 2009]
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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.
Cf. A000040. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 25 2009]
Sequence in context: A062157 A112347 A134824 this_sequence A014041 A015868 A015824
Adjacent sequences: A000004 A000005 A000006 this_sequence A000008 A000009 A000010
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KEYWORD
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core,easy,nonn,mult
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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