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A083337 a(n)=2a(n-1)+2a(n-2). 10
0, 3, 6, 18, 48, 132, 360, 984, 2688, 7344, 20064, 54816, 149760, 409152, 1117824, 3053952, 8343552, 22795008, 62277120, 170144256, 464842752, 1269974016, 3469633536, 9479215104, 25897697280, 70753824768 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n)=a(n-1)+3*A026150(n-1). a(n)/A026150(n) converges to sqrt(3).

LINKS

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

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

Tanya Khovanova, Recursive Sequences

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

FORMULA

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

a(n), n>0 = lower left term of [1,1; 3,1]^n - Gary W. Adamson, Mar 12 2008

a(n)=(1/2)*[1+sqrt(3)]^n*sqrt(3)-(1/2)*sqrt(3)*[1-sqrt(3)]^n, with n>=0 - Paolo P. Lava, Jun 10 2008

MATHEMATICA

CoefficientList[Series[3x/(1-2x-2x^2), {x, 0, 25}], x]

PROG

(Haskell)

a083337 n = a083337_list !! n

a083337_list =

   0 : 3 : map (* 2) (zipWith (+) a083337_list (tail a083337_list))

-- Reinhard Zumkeller, Oct 15 2011

CROSSREFS

Equals 3 * A002605.

Cf. A026150.

Cf. A028859, A028860, A030195, A080040, A106435, A108898, A125145.

Sequence in context: A148558 A148559 A108507 * A019308 A000932 A187124

Adjacent sequences:  A083334 A083335 A083336 * A083338 A083339 A083340

KEYWORD

easy,nonn

AUTHOR

Mario Catalani (mario.catalani(AT)unito.it), Apr 29 2003

STATUS

approved

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Last modified March 22 22:17 EDT 2017. Contains 283901 sequences.