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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

Table of n, a(n) for n=0..24.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 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.]

CROSSREFS

Sequence in context: A180147 A044049 A255284 * A086901 A003526 A121517

Adjacent sequences:  A005822 A005823 A005824 * A005826 A005827 A005828

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jeffrey Shallit

EXTENSIONS

Edited by R. J. Mathar, Mar 11 2009

STATUS

approved

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Last modified January 22 18:06 EST 2019. Contains 319365 sequences. (Running on oeis4.)