The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A006085 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A006085

Continued fraction for e/4.
(history; published version)

#29 by Bruno Berselli at Tue May 17 04:04:23 EDT 2016

STATUS

reviewed

approved

#28 by Michel Marcus at Mon May 16 15:04:07 EDT 2016

STATUS

proposed

reviewed

#27 by Colin Barker at Mon May 16 14:28:51 EDT 2016

STATUS

editing

proposed

#26 by Colin Barker at Mon May 16 14:28:36 EDT 2016

FORMULA

G.f.: x*(1+x+7*x^2-4*x^3+5*x^4-4*x^5+5*x^6-4*x^7+9*x^8-12*x^9-3*x^10-x^11-x^13-6*x^16+7*x^17+x^18) / ((1-x)^2*(1+x)*(1+x^2)^2*(1+x^4)^2). - Colin Barker, May 16 2016

PROG

(PARI) concat(0, Vec(x*(1+x+7*x^2-4*x^3+5*x^4-4*x^5+5*x^6-4*x^7+9*x^8-12*x^9-3*x^10-x^11-x^13-6*x^16+7*x^17+x^18)/((1-x)^2*(1+x)*(1+x^2)^2*(1+x^4)^2) + O(x^50))) \\ Colin Barker, May 16 2016

STATUS

approved

editing

#25 by Jon E. Schoenfield at Sun Dec 20 01:41:40 EST 2015

STATUS

editing

approved

#24 by Jon E. Schoenfield at Sun Dec 20 01:41:38 EST 2015

LINKS

Harry J. Smith, <a href="/A006085/b006085.txt">Table of n, a(n) for n = 1,...,20000</a>

EXAMPLE

0.679570457114761308840071867... = 0 + 1/(1 + 1/(2 + 1/(8 + 1/(3 + ...)))) [From _. - _Harry J. Smith_, May 10 2009]

PROG

(PARI) { allocatemem(932245000); default(realprecision, 40000); x=contfrac(exp(1)/4); for (n=1, 20000, write("b006085.txt", n, " ", x[n])); } [From _\\ _Harry J. Smith_, May 10 2009]

CROSSREFS

Cf. A019741 = Decimal expansion. [From _- _Harry J. Smith_, May 10 2009]

AUTHOR

N. J. A. Sloane.

STATUS

approved

editing

#23 by Ray Chandler at Thu Sep 03 12:26:29 EDT 2015

STATUS

editing

approved

#22 by Ray Chandler at Thu Sep 03 12:26:23 EDT 2015

LINKS

<a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1).

MATHEMATICA

Join[{0, 1, 2, 8, 3}, LinearRecurrence[{1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1}, {1, 1, 1, 1, 7, 1, 1, 2, 1, 1, 1, 2, 7, 1, 2}, 97]] (* Ray Chandler, Sep 03 2015 *)

STATUS

approved

editing

#21 by Charles R Greathouse IV at Thu Nov 21 12:45:52 EST 2013

MATHEMATICA

ContinuedFraction[E/4, 120] (* From _Harvey P. Dale, _, Apr 01 2011 *)

Discussion

Thu Nov 21

12:45

OEIS Server: https://oeis.org/edit/global/2062

#20 by Russ Cox at Fri Mar 30 18:38:35 EDT 2012

FORMULA

First seven terms are 0, 1, 2, 8, 3, 1, 1; then a(8k)=1, a(8k+1)=k, a(8k+2)=7, a(8k+3)=1, a(8k+4)=k, a(8k+5)=2, a(8k+6)=1, a(8k+7)=1. - _Benoit Cloitre (benoit7848c(AT)orange.fr), _, Apr 08 2003

Discussion

Fri Mar 30

18:38

OEIS Server: https://oeis.org/edit/global/216