login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A075848 2*n^2 + 9 is a square. 5
0, 6, 36, 210, 1224, 7134, 41580, 242346, 1412496, 8232630, 47983284, 279667074, 1630019160, 9500447886, 55372668156, 322735561050, 1881040698144, 10963508627814, 63900011068740, 372436557784626, 2170719335639016 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Lim. n-> Inf. a(n)/a(n-1) = 3 + 2*Sqrt(2).

REFERENCES

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, pp. 341-400.

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

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Tanya Khovanova, Recursive Sequences

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

Eric Weisstein's World of Mathematics, Pell Equation.

Index entries for linear recurrences with constant coefficients, signature (6,-1).

FORMULA

a(n) = [(3+2*Sqrt(2))^n - (3-2*Sqrt(2))^n] * [3/(2*Sqrt(2))]; a(n) = 6*a(n-1) - a(n-2).

a(n) = 6*A001109(n).

G.f.: 6x/(1-6x+x^2). [From Philippe Deléham, Nov 17 2008]

MATHEMATICA

LinearRecurrence[{6, -1}, {0, 6}, 30] (* Harvey P. Dale, Nov 28 2012 *)

CROSSREFS

Sequence in context: A269406 A269603 A027910 * A096979 A269464 A123887

Adjacent sequences:  A075845 A075846 A075847 * A075849 A075850 A075851

KEYWORD

nonn,easy

AUTHOR

Gregory V. Richardson, Oct 15 2002

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 12 00:07 EST 2018. Contains 318052 sequences. (Running on oeis4.)