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A176812 Expansion of 3*(1+x)/(1-2*x-5*x^2). 1

%I #18 Jun 13 2015 00:53:37

%S 3,9,33,111,387,1329,4593,15831,54627,188409,649953,2241951,7733667,

%T 26677089,92022513,317430471,1094973507,3777099369,13029066273,

%U 44943629391,155032590147,534783327249,1844729605233,6363375846711

%N Expansion of 3*(1+x)/(1-2*x-5*x^2).

%C Binomial transform of A026532 after dropping A026532(0). [From _R. J. Mathar_, Apr 27 2010]

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (2,5).

%F Binet form: a(n)=2^n*(((3 + Sqrt[6])/2)*((1 + Sqrt[6])/2)^n + ((3 - Sqrt[6])/2)*((1 - Sqrt[6])/2)^n) = 3*A180168(n).

%t a[n_] = 2^n*(((3 + Sqrt[ 6])/2)*((1 + Sqrt[6])/2)^n + ((3 - Sqrt[6])/2)*((1 - Sqrt[6])/2)^n); Table[FullSimplify[a[n]], {n, 0, 30}]

%t CoefficientList[Series[(-3(1+x))/(5x^2+2x-1),{x,0,40}],x] (* _Harvey P. Dale_, Feb 24 2011 *)

%K nonn,easy

%O 0,1

%A _Roger L. Bagula_, Apr 26 2010

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)