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A005825 Numerators in a worst case of a Jacobi symbol algorithm.
(Formerly M4404)
1
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; refs; listen; history; text; internal format)
OFFSET
0,3
REFERENCES
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).
LINKS
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 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.
FORMULA
a(n) = 5*a(n-1)-10*a(n-3)+4*a(n-4), by definition [R. J. Mathar, Mar 11 2009]
MAPLE
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.]
MATHEMATICA
LinearRecurrence[{5, 0, -10, 4}, {0, 1, 7, 31}, 30] (* Harvey P. Dale, Apr 11 2021 *)
CROSSREFS
Sequence in context: A180147 A044049 A255284 * A086901 A003526 A121517
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by R. J. Mathar, Mar 11 2009
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)