The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A202156 y-values in the solution to x^2 - 13*y^2 = -1. 3
5, 6485, 8417525, 10925940965, 14181862955045, 18408047189707445, 23893631070377308565, 31013914721302556809925, 40256037414619648361974085, 52252305550261582271285552405, 67823452348202119168480285047605, 88034788895660800419105138706238885 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The corresponding values of x of this Pell equation are in A202155.
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers: The Queen of Mathematics Entertains, Dover Publications (New York), 1966, p. 264.
LINKS
A. J. C. Cunningham, Binomial Factorisations, Vols. 1-9, Hodgson, London, 1923-1929. See Vol. 1, page xxxv.
Tanya Khovanova, Recursive Sequences.
A. M. S. Ramasamy, Polynomial solutions for the Pell's equation, Indian Journal of Pure and Applied Mathematics 25 (1994), p. 579 (Theorem 4, case t=1).
FORMULA
G.f.: 5*x*(1-x)/(1-1298*x+x^2).
a(n) = a(-n+1) = 5*(r^(2n-1)+1/r^(2n-1))/(r+1/r), where r=18+5*sqrt(13).
a(n) = A006191(6*n - 3). - Michael Somos, Feb 24 2023
MATHEMATICA
LinearRecurrence[{1298, -1}, {5, 6485}, 12]
PROG
(Magma) m:=13; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(5*x*(1-x)/(1-1298*x+x^2)));
(Maxima) makelist(expand(((18+5*sqrt(13))^(2*n-1)-(18-5*sqrt(13))^(2*n-1))/(2*sqrt(13))), n, 1, 12);
CROSSREFS
Sequence in context: A079812 A137694 A292334 * A117711 A203689 A116140
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Dec 15 2011
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 21 14:18 EDT 2024. Contains 372738 sequences. (Running on oeis4.)