A106567 a(n) = 5*a(n-1) + 4*a(n-2), with a(0) = 4, a(1) = 4.

0, 4, 20, 116, 660, 3764, 21460, 122356, 697620, 3977524, 22678100, 129300596, 737215380, 4203279284, 23965257940, 136639406836, 779058065940, 4441847957044, 25325472048980, 144394752073076, 823275648561300, 4693957251098804, 26762888849739220

Offset: 0

Author

Roger L. Bagula, May 30 2005

Keywords

• nonn
• easy
• less

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,4).

Crossrefs

Cf. A015537.

Programs

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

Mathematica

CoefficientList[Series[4*x/(1-5*x-4*x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Mar 22 2018 *)
LinearRecurrence[{5,4},{0,4},30] (* Harvey P. Dale, Jan 19 2025 *)

PARI

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

Sage

def A106567_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 4*x/(1-5*x-4*x^2) ).list()
A106567_list(30) # G. C. Greubel, Sep 06 2021

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

Extensions

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

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