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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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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
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OFFSET
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0,3
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REFERENCES
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Shallit, Jeffrey; On the worst case of three algorithms for computing the Jacobi symbol. J. Symbolic Comput. 10 (1990), no. 6, 593-610.
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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FORMULA
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a(n) = 5*a(n-1)-10*a(n-3)+4*a(n-4), by definition [R. J. Mathar, 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 Simon Plouffe in his 1992 dissertation.]
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MATHEMATICA
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LinearRecurrence[{5, 0, -10, 4}, {0, 1, 7, 31}, 30] (* Harvey P. Dale, Apr 11 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Edited by R. J. Mathar, Mar 11 2009
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STATUS
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approved
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