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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
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
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 March 28 07:33 EDT 2024. Contains 371235 sequences. (Running on oeis4.)