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
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