A005826 Worst case of a Jacobi symbol algorithm.

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

Author

N. J. A. Sloane, Jeffrey Shallit

Keywords

• nonn
• easy

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• 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).

Programs

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.]

Formula

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

Extensions

More terms from L. Edson Jeffery, Dec 07 2013