login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A195616 Denominators a(n) of Pythagorean approximations b(n)/a(n) to 3. 5
12, 444, 16872, 640680, 24328980, 923860548, 35082371856, 1332206269968, 50588755886940, 1921040517433740, 72948950906595192, 2770139093933183544, 105192336618554379492, 3994538652411133237140, 151687276455004508631840 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A195500 for a discussion and references.

LINKS

Colin Barker, Table of n, a(n) for n = 1..633

Index entries for linear recurrences with constant coefficients, signature (37,37,-1).

FORMULA

a(n) = 37*a(n-1)+37*a(n-2)-a(n-3). - Colin Barker, Jun 04 2015

G.f.: 12*x / ((x+1)*(x^2-38*x+1)). - Colin Barker, Jun 04 2015

MATHEMATICA

r = 3; z = 20;

p[{f_, n_}] := (#1[[2]]/#1[[

      1]] &)[({2 #1[[1]] #1[[2]], #1[[1]]^2 - #1[[

         2]]^2} &)[({Numerator[#1], Denominator[#1]} &)[

     Array[FromContinuedFraction[

        ContinuedFraction[(#1 + Sqrt[1 + #1^2] &)[f], #1]] &, {n}]]]];

{a, b} = ({Denominator[#1], Numerator[#1]} &)[

  p[{r, z}]]  (* A195616, A195617 *)

Sqrt[a^2 + b^2] (* A097315 *)

(* Peter J. C. Moses, Sep 02 2011 *)

PROG

(PARI) Vec(12*x/((x+1)*(x^2-38*x+1)) + O(x^20)) \\ Colin Barker, Jun 04 2015

CROSSREFS

Cf. A195500, A195617, A097315.

Sequence in context: A303922 A246502 A281248 * A126603 A291996 A192601

Adjacent sequences:  A195613 A195614 A195615 * A195617 A195618 A195619

KEYWORD

nonn,easy,frac

AUTHOR

Clark Kimberling, Sep 22 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 05:39 EDT 2020. Contains 333105 sequences. (Running on oeis4.)