The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A176981 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A176981

Expansion of 1+(1-2*x)/(-1+2*x+x^2).
(history; published version)

#25 by Charles R Greathouse IV at Sat Jun 13 00:53:37 EDT 2015

LINKS

<a href="/index/Rec">Index to sequences with entries for linear recurrences with constant coefficients</a>, signature (2,1).

Discussion

Sat Jun 13

00:53

OEIS Server: https://oeis.org/edit/global/2439

#24 by Charles R Greathouse IV at Fri Jun 12 15:27:27 EDT 2015

LINKS

<a href="/index/Rea#recLCCRec">Index to sequences with linear recurrences with constant coefficients</a>, signature (2,1).

Discussion

Fri Jun 12

15:27

OEIS Server: https://oeis.org/edit/global/2436

#23 by Charles R Greathouse IV at Wed Apr 30 01:32:59 EDT 2014

FORMULA

G.f.: 1 / (1 + x^2 / (1 - 2*x / (1 - x / (1 + x)))). - _Michael Somos, _, Jan 03 2013

Discussion

Wed Apr 30

01:32

OEIS Server: https://oeis.org/edit/global/2175

#22 by T. D. Noe at Wed Sep 11 12:59:11 EDT 2013

STATUS

proposed

approved

#21 by Sergei N. Gladkovskii at Sun Sep 08 14:56:33 EDT 2013

STATUS

editing

proposed

Discussion

Mon Sep 09

11:42

Joerg Arndt: Translation: "Well, not the most interesting CD ..."

12:40

Sergei N. Gladkovskii: да. ЦД=continued fraction

#20 by Sergei N. Gladkovskii at Sun Sep 08 14:55:50 EDT 2013

FORMULA

G.f.: 1 - Q(0)*x^2/2 , where Q(k) = 1 + 1/(1 - x*(4*k+2 + x)/( x*(4*k+4 + x) + 1/Q(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Sep 08 2013

STATUS

approved

editing

Discussion

Sun Sep 08

14:56

Sergei N. Gladkovskii: ну, не самые интересные ЦД...

#19 by Bruno Berselli at Thu Jan 03 07:57:47 EST 2013

STATUS

editing

approved

#18 by Bruno Berselli at Thu Jan 03 07:57:42 EST 2013

MATHEMATICA

a[0] = 1; a[n_] := a[n] = a[n - 1] - Sqrt[2*a[n - 1]^2 + (-1)^n]; Table[a[n], {n, 0, 30}]

a[n_] := a[n] = a[n - 1] - Sqrt[2*a[n - 1]^2 + (-1)^n];

TableJoin[a{1}, LinearRecurrence[n{2, 1}, {0, -1}, 30]], (* or *) Join[{1}, Rest[ CoefficientList[Series[1 + (1 - 2 x)/(-1 + 2 x + x^2), {n, x, 0, 30}] , x]]] (* _Harvey P. Dale_, Dec 24 2011 *)

Join[{1}, LinearRecurrence[{2, 1}, {0, -1}, 30]] (* or *) Join[{1}, Rest[ CoefficientList[Series[1+(1-2x)/(-1+2x+x^2), {x, 0, 30}], x]]] (* From Harvey P. Dale, Dec 24 2011 *)

CROSSREFS

Cf. A000129.

STATUS

proposed

editing

#17 by Vincenzo Librandi at Thu Jan 03 01:50:45 EST 2013

STATUS

editing

proposed

#16 by Vincenzo Librandi at Thu Jan 03 01:50:33 EST 2013

LINKS

<a href="/index/Rea#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (2,1).