The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A040132 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A040132

Continued fraction for sqrt(145).
(history; published version)

#21 by Michael De Vlieger at Tue Feb 13 08:16:31 EST 2024

STATUS

reviewed

approved

#20 by Michel Marcus at Tue Feb 13 01:26:04 EST 2024

STATUS

proposed

reviewed

#19 by Elmo R. Oliveira at Mon Feb 12 20:47:19 EST 2024

STATUS

editing

proposed

#18 by Elmo R. Oliveira at Mon Feb 12 20:41:46 EST 2024

FORMULA

From Elmo R. Oliveira, Feb 12 2024: (Start)

a(n) = 24 for n >= 1.

G.f.: 12*(1+x)/(1-x).

E.g.f.: 24*exp(x) - 12.

a(n) = 12*A040000(n) = 6*A040002(n) = 4*A040006(n). (End)

EXAMPLE

12 + 1/(24 + 1/(24 + 1/(24 + 1/(24 + ...)))) = sqrt(145).

CROSSREFS

Cf. A041264/A041265 (convergents), A176910 (decimal expansion).

Cf. A040000, A040002, A040006.

STATUS

approved

editing

#17 by Joerg Arndt at Wed Dec 27 00:09:11 EST 2023

STATUS

editing

approved

#16 by Joerg Arndt at Wed Dec 27 00:09:01 EST 2023

FORMULA

a(n)=24-12*[C(2*n,n) mod 2], with n>=0 [From Paolo P. Lava, Jun 10 2009]

STATUS

approved

editing

#15 by Ray Chandler at Thu Mar 09 18:59:38 EST 2017

STATUS

editing

approved

#14 by Ray Chandler at Thu Mar 09 18:59:35 EST 2017

LINKS

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

STATUS

approved

editing

#13 by Charles R Greathouse IV at Sun Aug 03 14:16:23 EDT 2014

MATHEMATICA

ContinuedFraction[Sqrt[145], 300] (*From _Vladimir Joseph Stephan Orlovsky, _, Mar 13 2011*)

Discussion

Sun Aug 03

14:16

OEIS Server: https://oeis.org/edit/global/2269

#12 by Russ Cox at Fri Mar 30 18:53:21 EDT 2012

FORMULA

a(n)=24-12*[C(2*n,n) mod 2], with n>=0 [From _Paolo P. Lava (paoloplava(AT)gmail.com), _, Jun 10 2009]

Discussion

Fri Mar 30

18:53

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