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.

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(11))*(10+3*sqrt(11))^n - (3-sqrt(11))*(10-3*sqrt(11))^n)/(2*sqrt(11)). - Dean Hickerson (dean(AT)math.ucdavis.edu), Dec 09 2002

G.f.: (1-x)/(1-20*x+x^2). a(n)=20*a(n-1)-a(n-2), n>1. - Michael Somos, Oct 29 2002

Let q(n, x)=sum(i=0, n, x^(n-i)*binomial(2*n-i, i)) then a(n)=q(n, 18). - Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 06 2002

G.f.: (1-x)/(1-20*x+x^2). a(n)=20*a(n-1)-a(n-2). a(-1-n)=a(n). - Michael Somos, Apr 18 2003

(PARI) a(n)=subst(poltchebi(n+1)+poltchebi(n), x, 10)/11

11a(n)^2-9*A083043(n)^2=2.

Row 20 of array A094954.

Cf. A075844.

Adjacent sequences: A075836 A075837 A075838 this_sequence A075840 A075841 A075842

Sequence in context: A057685 A041686 A023283 this_sequence A072359 A094737 A009075

easy,nonn

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