A005825 Numerators in a worst case of a Jacobi symbol algorithm. (Formerly M4404)

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

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

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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.

Index entries for linear recurrences with constant coefficients, signature (5,0,-10,4).

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: A044049 A378687 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