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A106567 a(n) = 5*a(n-1) + 4*a(n-2), with a(0) = 4, a(1) = 4. 1
0, 4, 20, 116, 660, 3764, 21460, 122356, 697620, 3977524, 22678100, 129300596, 737215380, 4203279284, 23965257940, 136639406836, 779058065940, 4441847957044, 25325472048980, 144394752073076, 823275648561300, 4693957251098804, 26762888849739220 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (5,4).

FORMULA

a(n) = 4*A015537(n).

From Chai Wah Wu, Mar 21 2018: (Start)

a(n) = 5*a(n-1) + 4*a(n-2) for n > 1.

G.f.: 4*x/(1 - 5*x - 4*x^2). (End)

a(n) = 4*(p^n - q^n)/(p - q), where 2*p = 5 + sqrt(41), 2*q = 5 - sqrt(41). - G. C. Greubel, Sep 06 2021

MATHEMATICA

CoefficientList[Series[4*x/(1-5*x-4*x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Mar 22 2018 *)

PROG

(Magma) I:=[0, 4]; [n le 2 select I[n] else 5*Self(n-1) +4*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Mar 22 2018

(PARI) a(n) = (([0, 4; 1, 5]^n)*[0, 1]~)[1]; \\ Michel Marcus, Mar 22 2018

(Sage)

def A106567_list(prec):

P.<x> = PowerSeriesRing(ZZ, prec)

return P( 4*x/(1-5*x-4*x^2) ).list()

A106567_list(30) # G. C. Greubel, Sep 06 2021

CROSSREFS

Cf. A015537.

Sequence in context: A192924 A258664 A231539 * A077445 A085458 A085456

Adjacent sequences: A106564 A106565 A106566 * A106568 A106569 A106570

KEYWORD

nonn,easy,less

AUTHOR

Roger L. Bagula, May 30 2005

EXTENSIONS

Edited by N. J. A. Sloane, Apr 30 2006

New name after Chai Wah Wu, by Bruno Berselli, Mar 22 2018

STATUS

approved

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Last modified December 2 18:40 EST 2022. Contains 358510 sequences. (Running on oeis4.)