A165749 a(n) = (9/5)*(1+4*(-9)^(n-1)).
1, 9, -63, 585, -5247, 47241, -425151, 3826377, -34437375, 309936393, -2789427519, 25104847689, -225943629183, 2033492662665, -18301433963967, 164712905675721, -1482416151081471, 13341745359733257
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..500
- Index entries for linear recurrences with constant coefficients, signature (-8, 9).
Programs
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Mathematica
Table[9/5 (1+4(-9)^(n-1)),{n,0,20}] (* or *) LinearRecurrence[{-8,9},{1,9},20] (* Harvey P. Dale, Nov 24 2011 *) -
PARI
x='x+O('x^99); Vec((1+17*x)/(1+8*x-9*x^2)) \\ Altug Alkan, Apr 07 2016 -
PARI
a(n) = (9-4*(-9)^n)/5 \\ Charles R Greathouse IV, Apr 07 2016
Formula
a(n) = -8*a(n-1) + 9*a(n-2), a(0)=1, a(1)=9.
a(n) = (-9)*a(n-1) + 18 for n>=1, with a(0)=1.
G.f.: (1+17x)/(1+8x-9x^2).
a(n) = Sum_{0<=k<=n} A112555(n,k)*8^(n-k).
E.g.f.: (1/5)*(9*exp(x) - 4*exp(-9*x)). - G. C. Greubel, Apr 07 2016