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A084059 a(n) = 4*a(n-1)+2*a(n-2) for n>1, a(0)=1, a(1)=2. 8
1, 2, 10, 44, 196, 872, 3880, 17264, 76816, 341792, 1520800, 6766784, 30108736, 133968512, 596091520, 2652303104, 11801395456, 52510188032, 233643543040, 1039594548224, 4625665278976, 20581850212352, 91578731407360 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A002533.

2*A084059 is the Lucas sequence V(4,-2). [Bruno Berselli, Jan 09 2013]

LINKS

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (4,2).

FORMULA

E.g.f.: exp(2*x)*cosh(sqrt(6)*x).

a(n) = ((2+sqrt(6))^n+(2-sqrt(6))^n)/2. - Paul Barry, May 13 2003

a(n) = sum(k=0..floor(n/2), C(n,2k)*2^(n-k)*3^k). - Paul Barry, Jan 15 2007

G.f.: (1-2x)/(1-4*x-2*x^2). [Philippe Deléham, Sep 07 2009]

a(n) = A090017(n+1)-2*A090017(n). - R. J. Mathar, Apr 05 2011

a(n) = sum(k=0..n, A201730(n,k)*5^k). - Philippe Deléham, Dec 06 2011

G.f.: G(0)/2, where G(k)= 1 + 1/(1 - x*(3*k-2)/(x*(3*k+1) - 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 27 2013

PROG

(Sage) [lucas_number2(n, 4, -2)/2 for n in xrange(0, 23)] # Zerinvary Lajos, May 14 2009

(MAGMA) [n le 2 select n else 4*Self(n-1)+2*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Apr 05 2011

(PARI) Vec((1-2*x)/(1-4*x-2*x^2) + O(x^30)) \\ Michel Marcus, Feb 04 2016

CROSSREFS

Cf. A090017.

Sequence in context: A068551 A099919 A100397 * A084609 A105485 A151313

Adjacent sequences:  A084056 A084057 A084058 * A084060 A084061 A084062

KEYWORD

nonn,easy

AUTHOR

Paul Barry, May 10 2003

STATUS

approved

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Last modified October 20 01:39 EDT 2018. Contains 316378 sequences. (Running on oeis4.)