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Search: id:A005825
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| A005825 |
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Numerators in a worst case of a Jacobi symbol algorithm.
(Formerly M4404)
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+0
1
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| 0, 1, 7, 31, 145, 659, 3013, 13739, 62685, 285931, 1304317, 5949691, 27139885, 123799979, 564720253, 2576001179, 11750565645, 53600825611, 244502997277, 1115313334651, 5087560679725, 23207176728299, 105860762284093, 482889457961819, 2202725765245005
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Shallit, Jeffrey; On the worst case of three algorithms for computing the Jacobi symbol. J. Symbolic Comput. 10 (1990), no. 6, 593-610.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Jeffrey Shallit, On the worst case of three algorithms for computing the Jacobi Symbol, J. Symbolic Comput. 10 (1990), no 6, 593-610, Variable R_n conjecture 6.2.
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FORMULA
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a(n) = 5*a(n-1)-10*a(n-3)+4*a(n-4), by definition [R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 11 2009]
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MAPLE
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A005825:=z*(-1-2*z+4*z**2)/(2*z**2-1)/(1-5*z+2*z**2); [Conjectured (correctly) by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Sequence in context: A033474 A001896 A044049 this_sequence A086901 A003526 A121517
Adjacent sequences: A005822 A005823 A005824 this_sequence A005826 A005827 A005828
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jeffrey Shallit
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EXTENSIONS
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Edited by R. J. Mathar, Mar 11 2009
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