1,1

Lim. n-> Inf. a(n)/a(n-1) = phi^6 = 9 + 4*Sqrt(5).

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.

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) = 3*sqrt(5)/10*((2+sqrt(5))^(2*n-1)-(2-sqrt(5))^(2*n-1)) = 18*a(n-1) - a(n-2)

Cf. 3*A007805.

Sequence in context: A071094 A062216 A045489 this_sequence A126685 A105639 A003028

Adjacent sequences: A075866 A075867 A075868 this_sequence A075870 A075871 A075872

nonn

Gregory V. Richardson (omomom(AT)hotmail.com), Oct 16 2002