A168075 - OEIS

%I #21 Mar 03 2024 15:52:32

%S 1,-3,36,-189,567,-2430,9477,-28431,104976,-373977,1121931,-3897234,

%T 13286025,-39858075,133923132,-444816117,1334448351,-4390765542,

%U 14334558093,-43003674279,139471376040,-449795187729,1349385563187,-4330586226042,13839047287569

%N Expansion of (1+27x^2-54x^3)/((1+3x)^2*(1-3x+9 x^2)).

%C Hankel transform of A168076.

%H G. C. Greubel, <a href="/A168075/b168075.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-3,0,-27,-81).

%F a(n) = (-3)^n*A061891(n).

%F a(n) = 2*(-3)^n*n + 3^n*(sin(Pi*n/3)/sqrt(3) + cos(Pi*n/3)). - _Ilya Gutkovskiy_, Jul 10 2016

%t LinearRecurrence[{-3, 0, -27, -81}, {1, -3, 36, -189}, 50] (* _G. C. Greubel_, Jul 09 2016 *)

%t CoefficientList[Series[(1 + 27 x^2 - 54 x^3) / ((1 + 3 x)^2 (1 - 3 x + 9 x^2)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jul 10 2016 *)

%o (PARI) Vec((1+27*x^2-54*x^3)/((1+3*x)^2*(1-3*x+9*x^2))+ O(x^30)) \\ _Michel Marcus_, Dec 03 2014

%o (Magma) I:=[1,-3,36,-189]; [n le 4 select I[n] else -3*Self(n-1)-27*Self(n-3)-81*Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Jul 10 2016

%Y Cf. A061891, A168076.

%K easy,sign

%O 0,2

%A _Paul Barry_, Nov 18 2009

%E Corrected by _R. J. Mathar_, Dec 03 2014