login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A214733 a(n) = - a(n-1) - 3*a(n-2), with a(0) = 0 and a(1) = 1. 3
0, 1, -1, -2, 5, 1, -16, 13, 35, -74, -31, 253, -160, -599, 1079, 718, -3955, 1801, 10064, -15467, -14725, 61126, -16951, -166427, 217280, 282001, -933841, 87838, 2713685, -2977199, -5163856, 14095453, 1396115, -43682474, 39494129, 91553293, -210035680 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The sequence a(n) is conjugate with A110523 by the following alternative relations: either ((-1 + i*sqrt(11))/2)^n = A110523(n) + a(n)*(-1 + i*sqrt(11))/2, or ((-1 - i*sqrt(11))/2)^n = A110523(n) + a(n)*(-1 - i*sqrt(11))/2 (see also comments to A110523, where these relations and many other facts on a(n) is presented).

Apart from signs, the Lucas U(P=1,Q=3)-sequence. - R. J. Mathar, Oct 24 2012

REFERENCES

R. Witula, On Some Applications of Formulae for Unimodular Complex Numbers, Jacek Skalmierski's Press, Gliwice 2011.

LINKS

Table of n, a(n) for n=0..36.

Wikipedia, Lucas sequence

FORMULA

a(n+2) = - a(n+1) - 3a(n).

a(n) = (i*sqrt(11)/11)*(((-1 - i*sqrt(11))/2)^n - ((-1 + i*sqrt(11))/2)^n).

G.f.: x/(1 + x + 3*x^2).

G.f.: Q(0) -1, where Q(k) = 1 - 3*x^2 - (k+2)*x + x*(k+1 + 3*x)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 07 2013

MATHEMATICA

LinearRecurrence[{-1, -3}, {0, 1}, 40] (* T. D. Noe, Jul 30 2012 *)

PROG

(PARI) concat(0, Vec(1/(1+x+3*x^2)+O(x^99))) \\ Charles R Greathouse IV, Oct 01 2012

CROSSREFS

Cf. A106852, A110523.

Sequence in context: A186361 A197365 A121579 * A106852 A162975 A187244

Adjacent sequences:  A214730 A214731 A214732 * A214734 A214735 A214736

KEYWORD

sign,easy

AUTHOR

Roman Witula, Jul 27 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 27 09:02 EST 2014. Contains 250176 sequences.