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A195614 Denominators a(n) of Pythagorean approximations b(n)/a(n) to 2. 3
8, 136, 2448, 43920, 788120, 14142232, 253772064, 4553754912, 81713816360, 1466294939560, 26311595095728, 472142416783536, 8472251907007928, 152028391909359160, 2728038802461456960, 48952670052396866112, 878420022140682133064 (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..797

Index entries for linear recurrences with constant coefficients, signature (17,17,-1).

FORMULA

a(n) = 17*a(n-1)+17*a(n-2)-a(n-3). G.f.: 8*x / ((x+1)*(x^2-18*x+1)). - Colin Barker, Jun 04 2015

a(n) = (-4*(-1)^n-(-2+sqrt(5))*(9+4*sqrt(5))^(-n)+(2+sqrt(5))*(9+4*sqrt(5))^n)/10. - Colin Barker, Mar 04 2016

MATHEMATICA

r = 2; z = 32;

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}]]  (* A195614, A195615 *)

Sqrt[a^2 + b^2] (* A007805 *)

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

PROG

(PARI) Vec(8*x/((x+1)*(x^2-18*x+1)) + O(x^50)) \\ Colin Barker, Jun 04 2015

CROSSREFS

Cf. A195500, A195615, A007805.

Sequence in context: A291699 A292914 A072072 * A131927 A132869 A036915

Adjacent sequences:  A195611 A195612 A195613 * A195615 A195616 A195617

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Sep 22 2011

STATUS

approved

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Last modified April 9 20:46 EDT 2020. Contains 333363 sequences. (Running on oeis4.)