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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A080040 a(n) = 2*a(n-1) + 2*a(n-2) with n>1, a(0)=2, a(1)=2. 32
2, 2, 8, 20, 56, 152, 416, 1136, 3104, 8480, 23168, 63296, 172928, 472448, 1290752, 3526400, 9634304, 26321408, 71911424, 196465664, 536754176, 1466439680, 4006387712, 10945654784, 29904084992, 81699479552, 223207129088 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The Lucas sequence V_n(2,-2). - Jud McCranie, Mar 02 2012

The signed version 2, -2, 8, -20, 56, -152, 416, -1136, 3104, -8480, 23168,... is the Lucas sequence V(-2,-2). - R. J. Mathar, Jan 08 2013

After a(2) equals round((1+sqrt(3))^n) = 1, 3, 7, 20, 56, 152, ... - Jeremy Gardiner, Aug 11 2013

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

I. Amburg, K. Dasaratha, L. Flapan, T. Garrity, C. Lee, C. Mihailak, N. Neumann-Chun, S. Peluse, M. Stoffregen, Stern Sequences for a Family of Multidimensional Continued Fractions: TRIP-Stern Sequences, arXiv:1509.05239v1 [math.CO] 17 Sep 2015.

Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.

D. Jhala, G. P. S. Rathore, K. Sisodiya, Some Properties of k-Jacobsthal Numbers with Arithmetic Indexes, Turkish Journal of Analysis and Number Theory, 2014, Vol. 2, No. 4, 119-124.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (2,2).

Index entries for Lucas sequences (2,-2).

FORMULA

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

a(n) = (1+sqrt(3))^n+(1-sqrt(3))^n.

a(n) = 2*A026150(n). -Philippe Deléham, Nov 19 2008

G.f.: G(0), where G(k)= 1 + 1/(1 - x*(3*k-1)/(x*(3*k+2) - 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 11 2013

a(n) = 2*2^floor(n/2)*A002531(n). - Ralf Stephan, Sep 08 2013

a(n) = [x^n] ( 1 + x + sqrt(1 + 2*x + 3*x^2) )^n for n >= 1. - Peter Bala, Jun 29 2015

MATHEMATICA

CoefficientList[Series[(2 - 2t)/(1 - 2t - 2t^2), {t, 0, 30}], t]

With[{c={2, 2}}, LinearRecurrence[c, c, 20]] (* Harvey P. Dale, Apr 24 2016 *)

Round@Table[LucasL[n, Sqrt[2]] 2^(n/2), {n, 0, 20}] (* Vladimir Reshetnikov, Sep 15 2016 *)

PROG

(Sage) from sage.combinat.sloane_functions import recur_gen2b; it = recur_gen2b(2, 2, 2, 2, lambda n: 0); [it.next() for i in range(27)] # Zerinvary Lajos, Jul 16 2008

(Sage) [lucas_number2(n, 2, -2) for n in xrange(0, 27)] # Zerinvary Lajos, Apr 30 2009

(Haskell)

a080040 n = a080040_list !! n

a080040_list =

   2 : 2 : map (* 2) (zipWith (+) a080040_list (tail a080040_list))

-- Reinhard Zumkeller, Oct 15 2011

(PARI) a(n)=([0, 1; 2, 2]^n*[2; 2])[1, 1] \\ Charles R Greathouse IV, Apr 08 2016

CROSSREFS

Cf. A002605, A028859, A030195, A083337, A106435, A108898, A125145.

Sequence in context: A067640 A098277 A242658 * A060823 A178076 A259807

Adjacent sequences:  A080037 A080038 A080039 * A080041 A080042 A080043

KEYWORD

easy,nonn

AUTHOR

Mario Catalani (mario.catalani(AT)unito.it), Jan 21 2003

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy .

Last modified March 25 01:30 EDT 2017. Contains 284036 sequences.