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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A075835 Numbers n such that 13*n^2 + 4 is a square. 1
0, 3, 33, 360, 3927, 42837, 467280, 5097243, 55602393, 606529080, 6616217487, 72171863277, 787274278560, 8587845200883, 93679022931153, 1021881407041800, 11147016454528647, 121595299592773317 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Lim. n-> Inf. a(n)/a(n-1) = (11 + Sqrt(13))/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.

S. Falcon, Relationships between Some k-Fibonacci Sequences, Applied Mathematics, 2014, 5, 2226-2234; http://www.scirp.org/journal/am; http://dx.doi.org/10.4236/am.2014.515216

LINKS

Table of n, a(n) for n=1..18.

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 (11,-1).

FORMULA

a(n) = [(11 + 3*Sqrt(13))^n - (11 - 3*Sqrt(13))^n] / [(2^n) * Sqrt(13)]

a(n) = 11*a(n-1)-a(n-2)with a(1)=0 and a(2)=3. G.f.: 3x^2/(1-11x+x^2). [From Philippe Deléham, Nov 17 2008]

a(n) = A006190(2*n). - Vladimir Reshetnikov, Sep 16 2016

MATHEMATICA

LinearRecurrence[{11, -1}, {0, 3}, 20] (* Harvey P. Dale, Dec 27 2011 *)

Table[Fibonacci[2n, 3], {n, 0, 20}] (* Vladimir Reshetnikov, Sep 16 2016 *)

CROSSREFS

Cf. A006190.

Sequence in context: A001507 A221162 A231594 * A077698 A080488 A082778

Adjacent sequences:  A075832 A075833 A075834 * A075836 A075837 A075838

KEYWORD

nonn,easy

AUTHOR

Gregory V. Richardson, Oct 14 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified June 28 16:56 EDT 2017. Contains 288839 sequences.