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A135522 a(n) = 2*a(n-1) + 3*a(n-2), with a(0) = 2 and a(1) = 3. 15

%I

%S 2,3,12,33,102,303,912,2733,8202,24603,73812,221433,664302,1992903,

%T 5978712,17936133,53808402,161425203,484275612,1452826833,4358480502,

%U 13075441503,39226324512,117678973533,353036920602,1059110761803

%N a(n) = 2*a(n-1) + 3*a(n-2), with a(0) = 2 and a(1) = 3.

%C Also: inverse binomial transform of A135520. - _R. J. Mathar_, Apr 17 2008

%H Vincenzo Librandi, <a href="/A135522/b135522.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,3).

%F From _R. J. Mathar_, Feb 23 2008: (Start)

%F O.g.f.: (5/(1-3*x) + 3/(1+x))/4.

%F a(n) = (5*3^n + 3*(-1)^n)/4. (End)

%F G.f.: (x-2)/(3*x^2 + 2*x - 1). - _Harvey P. Dale_, Mar 14 2011

%F E.g.f.: (1/4)*(5*exp(3*x) + 3*exp(-x)). - _G. C. Greubel_, Oct 17 2016

%t f[n_]:=3/(n+2);x=2;Table[x=f[x];Numerator[x],{n,0,5!}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 11 2010 *)

%t Transpose[NestList[Join[Rest[#],ListCorrelate[{3,2},#]]&, {2,3},30]][[1]] (* _Harvey P. Dale_, Mar 14 2011 *)

%t CoefficientList[Series[(x-2)/(3x^2+2x-1),{x,0,30}],x] (* _Harvey P. Dale_, Mar 14 2011 *)

%o (PARI) a(n)=(5*3^n+3*(-1)^n)/4 \\ _Charles R Greathouse IV_, Jun 01 2011

%o (MAGMA) [(5*3^n+3*(-1)^n)/4: n in [0..40]]; // _Vincenzo Librandi_, Jun 02 2011

%Y Cf. A060925.

%K nonn,easy

%O 0,1

%A _Paul Curtz_, Feb 19 2008

%E More terms from _R. J. Mathar_, Feb 23 2008

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Last modified May 17 11:46 EDT 2021. Contains 343971 sequences. (Running on oeis4.)