A005826 Worst case of a Jacobi symbol algorithm. (Formerly M3961)

1, 5, 31, 141, 659, 3005, 13739, 62669, 285931, 1304285, 5949691, 27139821, 123799979, 564720125, 2576001179, 11750565389, 53600825611, 244502996765, 1115313334651, 5087560678701, 23207176728299, 105860762282045, 482889457961819, 2202725765240909

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..23.

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 S_n conjecture 6.2.

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

Formula

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

Maple

A005826:=(-1-6*z**2+4*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: A184446 A077719 A235462 * A293716 A294692 A047109

Adjacent sequences: A005823 A005824 A005825 * A005827 A005828 A005829

Keyword

nonn,easy

Author

N. J. A. Sloane, Jeffrey Shallit

Extensions

More terms from L. Edson Jeffery, Dec 07 2013

Status

approved