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.

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

G.f.: 3x*(1-3x)/(1-18x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 17 2008]

Cf. 3*A007805.

Sequence in context: A062216 A045489 A145242 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