|
%I M2941 #29 Apr 13 2022 13:25:18
%S 1,3,13,57,259,1177,5367,24473,111631,509193,2322703,10595097,
%T 48330079,220460137,1005640527,4587282233,20925130111,95451085833,
%U 435405168943,1986123672537,9059808024799,41326792777897,188514347839887,859918153641593,3922562072528191,17892974055353673
%N Worst case of a Jacobi symbol algorithm.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H J. Shallit, <a href="http://dx.doi.org/10.1016/S0747-7171(08)80160-5">On the worst case of three algorithms for computing the Jacobi symbol</a>, J. Symbolic Comput. 10 (1990), no. 6, 593-610, Variable T_n conjecture 6.2.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5, 0, -10, 4).
%F a(n)=5a(n-1)-10a(n-3)+4a(n-4) by definition [_R. J. Mathar_, Mar 11 2009]
%p 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.]
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, _Jeffrey Shallit_
%E More terms from R. J. Mathar, Mar 11 2009
|
