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Revision History for A040650

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Showing entries 1-10 | older changes

A040650

Continued fraction for sqrt(677).
(history; published version)

#18 by Peter Luschny at Fri Feb 16 05:49:50 EST 2024

STATUS

reviewed

approved

#17 by Michel Marcus at Fri Feb 16 00:02:04 EST 2024

STATUS

proposed

reviewed

#16 by Elmo R. Oliveira at Thu Feb 15 18:34:20 EST 2024

STATUS

editing

proposed

#15 by Elmo R. Oliveira at Thu Feb 15 18:28:22 EST 2024

FORMULA

From Elmo R. Oliveira, Feb 15 2024: (Start)

a(n) = 52 for n >= 1.

G.f.: 26*(1+x)/(1-x).

E.g.f.: 52*exp(x) - 26.

a(n) = 26*A040000(n) = 13*A040002(n) = 2*A040156(n). (End)

EXAMPLE

26 + 1/(52 + 1/(52 + 1/(52 + 1/(52 + ...)))) = sqrt(677).

CROSSREFS

Cf. A042300/A042301 (convergents).

Cf. A040000, A040002, A040156.

AUTHOR

N. J. A. Sloane.

STATUS

approved

editing

#14 by Joerg Arndt at Wed Dec 27 00:23:15 EST 2023

STATUS

editing

approved

#13 by Joerg Arndt at Wed Dec 27 00:23:14 EST 2023

FORMULA

a(n)=52-25*[C(2*n,n) mod 2], with n>=0 [From Paolo P. Lava, May 18 2009]

STATUS

approved

editing

#12 by Ray Chandler at Fri Mar 10 14:39:56 EST 2017

STATUS

editing

approved

#11 by Ray Chandler at Fri Mar 10 14:39:54 EST 2017

LINKS

<a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).

STATUS

approved

editing

#10 by Russ Cox at Fri Mar 30 18:53:24 EDT 2012

FORMULA

a(n)=52-25*[C(2*n,n) mod 2], with n>=0 [From _Paolo P. Lava (paoloplava(AT)gmail.com), _, May 18 2009]

Discussion

Fri Mar 30

18:53

OEIS Server: https://oeis.org/edit/global/262

#9 by Russ Cox at Fri Mar 30 16:47:58 EDT 2012

AUTHOR

_N. J. A. Sloane (njas(AT)research.att.com)_.

Discussion

Fri Mar 30

16:47

OEIS Server: https://oeis.org/edit/global/110