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A014113 a(n) = a(n-1) + 2*a(n-2) with a(0)=0, a(1)=2. 5
0, 2, 2, 6, 10, 22, 42, 86, 170, 342, 682, 1366, 2730, 5462, 10922, 21846, 43690, 87382, 174762, 349526, 699050, 1398102, 2796202, 5592406, 11184810, 22369622, 44739242, 89478486, 178956970, 357913942 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 457

Index entries for linear recurrences with constant coefficients, signature (1,2).

FORMULA

a(0) = 0 and if n>=1, a(n) = 2^n - a(n-1).

a(n) = A078008(n+1). - Reinhard Zumkeller, Jun 10 2005

a(n) = 2*A001045(n). - Benoit Jubin, Dec 01 2011

a(n) = (2^(n+1) - 2*(-1)^n)/3. - Ralf Stephan, Jul 18 2013

G.f.: 2*x/(1+x)/(1-2*x). - Colin Barker, Feb 19 2012

G.f.: 1/Q(0) -1, where Q(k) = 1 + 2*x^2 - (2*k+3)*x + x*(2*k+1 - 2*x)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 05 2013

MATHEMATICA

LinearRecurrence[{1, 2}, {0, 2}, 50] (* Vincenzo Librandi, Feb 19 2012 *)

PROG

(Haskell)

a014113 n = a014113_list !! n

a014113_list = 0 : 2 : zipWith (+)

                       (map (* 2) a014113_list) (tail a014113_list)

-- Reinhard Zumkeller, Jul 20 2013

CROSSREFS

Cf. A163271, A001045, A078008.

Sequence in context: A167399 A247326 A019310 * A078008 A151575 A284462

Adjacent sequences:  A014110 A014111 A014112 * A014114 A014115 A014116

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 18 03:16 EDT 2017. Contains 290682 sequences.