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A005827 Worst case of a Jacobi symbol algorithm.
(Formerly M2941)
1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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..25.

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.

J. Shallit, On the 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 A151223

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

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Last modified January 19 18:27 EST 2019. Contains 319309 sequences. (Running on oeis4.)