The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A040590 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A040590

Continued fraction for sqrt(615).
(history; published version)

#18 by Joerg Arndt at Wed Dec 27 00:47:37 EST 2023

STATUS

proposed

approved

#17 by Amiram Eldar at Wed Dec 27 00:21:27 EST 2023

STATUS

editing

proposed

#16 by Amiram Eldar at Wed Dec 27 00:18:21 EST 2023

LINKS

<a href="/index/Con#confC">Index entries for continued fractions for constants</a>.

<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 1).

FORMULA

a(n)=(1/24)*{-229*(n mod 4)+65*[(n+1) mod 4]+41*[(n+2) mod 4]+335*[(n+3) mod 4]}-24*[C(2*n,n) mod 2], with n>=0 [From Paolo P. Lava, May 15 2009]

From Amiram Eldar, Dec 27 2023: (Start)

Multiplicative with a(2) = 3, a(2^e) = 48 for e >= 2, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 1/2^(s-1) + 45/2^(2*s)). (End)

KEYWORD

nonn,cofr,easy,less,mult

AUTHOR

N. J. A. Sloane.

STATUS

approved

editing

#15 by Harvey P. Dale at Wed Feb 02 14:56:15 EST 2022

STATUS

editing

approved

#14 by Harvey P. Dale at Wed Feb 02 14:56:13 EST 2022

MATHEMATICA

ContinuedFraction[Sqrt[615], 100] (* or *) PadRight[{24}, 100, {48, 1, 3, 1}] (* Harvey P. Dale, Feb 02 2022 *)

STATUS

approved

editing

#13 by Ray Chandler at Fri Mar 10 14:25:26 EST 2017

STATUS

editing

approved

#12 by Ray Chandler at Fri Mar 10 14:25:12 EST 2017

LINKS

<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 1).

STATUS

approved

editing

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

FORMULA

a(n)=(1/24)*{-229*(n mod 4)+65*[(n+1) mod 4]+41*[(n+2) mod 4]+335*[(n+3) mod 4]}-24*[C(2*n,n) mod 2], with n>=0 [From _Paolo P. Lava (paoloplava(AT)gmail.com), _, May 15 2009]

Discussion

Fri Mar 30

18:53

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

#10 by Russ Cox at Fri Mar 30 16:47:57 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

#9 by T. D. Noe at Wed Sep 28 20:46:18 EDT 2011

FORMULA

a(n)=(1/24)*{-229*(n mod 4)+65*[(n+1) mod 4]+41*[(n+2) mod 4]+335*[(n+3) mod 4]}-24*[C(2*n,n) mod 2], with n>=0 [From Paolo P. Lava (pplpaoloplava(AT)splgmail.atcom), May 15 2009]

Discussion

Wed Sep 28

20:46

OEIS Server: https://oeis.org/edit/global/96