0,2

Lim. n-> Inf. a(n)/a(n-1) = 10 + 3*Sqrt(11).

A. H. Beiler, "The Pellian", ch. 22 in Recreations in the Theory of Numbers: The Queen of Mathematics Entertains. Dover, New York, New York, pp. 248-268, 1966.

L. E. Dickson, History of the Theory of Numbers, Vol. II, Diophantine Analysis. AMS Chelsea Publishing, Providence, Rhode Island, 1999, p. 341-400.

Peter G. L. Dirichlet, Lectures on Number Theory (History of Mathematics Source Series, V. 16); American Mathematical Society, Providence, Rhode Island, 1999, p. 139-147.

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

J. J. O'Connor and E. F. Robertson, Pell's Equation

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

a(n) = [(10+3*Sqrt(11))^n - (10-3*Sqrt(11))^n] / Sqrt(11); a(n) = 20*a(n-1) - a(n-2).

G.f.: 6x / (1 - 20x + x^2).

Equals (1/3)[A075839(n+1)-A075839(n)].

Sequence in context: A001516 A026337 A065888 this_sequence A029697 A126448 A126446

Adjacent sequences: A075841 A075842 A075843 this_sequence A075845 A075846 A075847

nonn

Gregory V. Richardson (omomom(AT)hotmail.com), Oct 14 2002