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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A019431 Continued fraction for tan(1/8). 3
0, 7, 1, 22, 1, 38, 1, 54, 1, 70, 1, 86, 1, 102, 1, 118, 1, 134, 1, 150, 1, 166, 1, 182, 1, 198, 1, 214, 1, 230, 1, 246, 1, 262, 1, 278, 1, 294, 1, 310, 1, 326, 1, 342, 1, 358, 1, 374, 1, 390, 1, 406, 1, 422, 1, 438, 1, 454, 1, 470, 1, 486, 1, 502, 1, 518, 1, 534, 1, 550, 1, 566, 1, 582 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..20000

G. Xiao, Contfrac

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

FORMULA

From Colin Barker, Sep 08 2013: (Start)

a(n) = (-1+3*(-1)^n-8*(-1+(-1)^n)*n)/2 for n>1.

a(n) = 2*a(n-2)-a(n-4) for n>5.

G.f.: x*(x^4-x^3+8*x^2+x+7) / ((x-1)^2*(x+1)^2). (End)

EXAMPLE

0.12565513657513096779267821... = 0 + 1/(7 + 1/(1 + 1/(22 + 1/(1 + ...)))). - Harry J. Smith, Jun 14 2009

MATHEMATICA

Join[{0, 7}, LinearRecurrence[{0, 2, 0, -1}, {1, 22, 1, 38}, 100]] (* Vincenzo Librandi, Jan 03 2016 *)

PROG

(PARI) { allocatemem(932245000); default(realprecision, 97000); x=contfrac(tan(1/8)); for (n=0, 20000, write("b019431.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 14 2009

(PARI) Vec(x*(x^4-x^3+8*x^2+x+7)/((x-1)^2*(x+1)^2) + O(x^100)) \\ Colin Barker, Sep 08 2013

(MAGMA) [0, 7] cat [(-1+3*(-1)^n-8*(-1+(-1)^n)*n)/2: n in [2..80]] (* Vincenzo Librandi, Jan 03 2016 *)

CROSSREFS

Cf. A161017 (decimal expansion). - Harry J. Smith, Jun 14 2009

Sequence in context: A274717 A050310 A178445 * A264615 A261248 A214686

Adjacent sequences:  A019428 A019429 A019430 * A019432 A019433 A019434

KEYWORD

nonn,cofr,easy

AUTHOR

David W. Wilson

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 June 19 11:41 EDT 2019. Contains 324219 sequences. (Running on oeis4.)