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 A185940 a(n) = 1 - 2^(n+1) + 3^(n+2). 1

%I

%S 24,74,228,698,2124,6434,19428,58538,176124,529394,1590228,4774778,

%T 14332524,43013954,129074628,387289418,1161999324,3486260114,

%U 10459304628,31378962458,94138984524,282421147874,847271832228,2541832273898,7625530376124,22876658237234

%N a(n) = 1 - 2^(n+1) + 3^(n+2).

%H G. C. Greubel, <a href="/A185940/b185940.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).

%F a(n) = 1 - A000079(n+1) + A000244(n+2)

%F From _Alexander R. Povolotsky_, Jan 07 2011: (Start)

%F G.f.: 2*x*(12 - 35*x + 24*x^2) / (1 - 6*x + 11*x^2 - 6*x^3)

%F a(n+2) = -6*a(n) + 5*a(n+1)+2. (End)

%F a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3). - _G. C. Greubel_, Feb 25 2017

%F E.g.f.: exp(x) - 2*exp(2*x) + 9*exp(3*x) - 8. - _G. C. Greubel_, Jul 23 2017

%p A185940:=n->1-2^(n+1)+3^(n+2): seq(A185940(n), n=1..40); # _Wesley Ivan Hurt_, Jul 23 2017

%t CoefficientList[Series[-2*x*(12 - 35*x + 24*x^2)/(-1 + 6*x - 11*x^2 + 6*x^3), {x,0,50}], x] (* or *) LinearRecurrence[{6, -11, 6}, {24, 74, 228}, 50] (* _G. C. Greubel_, Feb 25 2017 *)

%o (MAGMA) [1 - 2^(n+1) + 3^(n+2): n in [1..40]]; // _Vincenzo Librandi_, Apr 05 2011

%o (PARI) x='x+O('x^50); Vec(-2*x*(12 - 35*x + 24*x^2) / (-1 + 6*x - 11*x^2 + 6*x^3)) \\ _G. C. Greubel_, Feb 25 2017

%Y Cf. A000079, A000244, A066280.

%K nonn,easy

%O 1,1

%A _Amir H. Farrahi_, Feb 06 2011

%E Corrected and edited by _Bruno Berselli_, Apr 04 2011

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Last modified July 25 02:42 EDT 2021. Contains 346282 sequences. (Running on oeis4.)