A005827 Worst case of a Jacobi symbol algorithm. (Formerly M2941)

1, 3, 13, 57, 259, 1177, 5367, 24473, 111631, 509193, 2322703, 10595097, 48330079, 220460137, 1005640527, 4587282233, 20925130111, 95451085833, 435405168943, 1986123672537, 9059808024799, 41326792777897, 188514347839887, 859918153641593, 3922562072528191, 17892974055353673

Offset

0,2

References

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..25.

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

J. Shallit, On the worst case of three algorithms for computing the Jacobi symbol, J. Symbolic Comput. 10 (1990), no. 6, 593-610, Variable T_n conjecture 6.2.

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

Formula

a(n)=5a(n-1)-10a(n-3)+4a(n-4) by definition [R. J. Mathar, Mar 11 2009]

Maple

A005827:=-(1-2*z-2*z**2+2*z**3)/(2*z**2-1)/(1-5*z+2*z**2); [Conjectured (correctly) by Simon Plouffe in his 1992 dissertation.]

Crossrefs

Sequence in context: A163606 A115968 A256939 * A151319 A151222 A349299

Adjacent sequences: A005824 A005825 A005826 * A005828 A005829 A005830

Keyword

nonn,easy

Author

N. J. A. Sloane, Jeffrey Shallit

Extensions

More terms from R. J. Mathar, Mar 11 2009

Status

approved