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A106567
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a(n) = 5*a(n-1) + 4*a(n-2), with a(0) = 4, a(1) = 4.
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1
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0, 4, 20, 116, 660, 3764, 21460, 122356, 697620, 3977524, 22678100, 129300596, 737215380, 4203279284, 23965257940, 136639406836, 779058065940, 4441847957044, 25325472048980, 144394752073076, 823275648561300, 4693957251098804, 26762888849739220
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OFFSET
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0,2
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LINKS
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FORMULA
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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
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MATHEMATICA
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CoefficientList[Series[4*x/(1-5*x-4*x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Mar 22 2018 *)
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PROG
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(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)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 4*x/(1-5*x-4*x^2) ).list()
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CROSSREFS
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KEYWORD
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nonn,easy,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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