A168072 Expansion of (1-27x^2-108x^3)/((1-3x)^2*(1+3x+9x^2)).

1, 3, -18, -135, -405, -1944, -8019, -24057, -91854, -334611, -1003833, -3542940, -12223143, -36669429, -124357194, -416118303, -1248354909, -4132485216, -13559717115, -40679151345, -132497807238, -428874481323, -1286623443969, -4142299868388

Offset

0,2

Comments

Hankel transform of A168073.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,0,27,-81).

Formula

a(n) = 3^n*A168071(n).

a(n) = 3^n*(sin(2*Pi*n/3)/sqrt(3) - cos(2*Pi*n/3) - 2*n + 2). - Ilya Gutkovskiy, Jul 10 2016

Mathematica

LinearRecurrence[{3, 0, 27, -81}, {1, 3, -18, -135}, 50] (* G. C. Greubel, Jul 09 2016 *)
CoefficientList[Series[(1 - 27 x^2 - 108 x^3) / ((1 - 3 x)^2 (1 + 3 x + 9 x^2)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 10 2016 *)

Prog

(PARI) Vec((1-27*x^2-108*x^3)/((1-3*x)^2*(1+3*x+9*x^2)) + O(x^30)) \\ Michel Marcus, Dec 03 2014
(Magma) I:=[1, 3, -18, -135]; [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

Crossrefs

Cf. A168071, A168073.

Sequence in context: A060909 A074545 A192462 * A251733 A355103 A355105

Adjacent sequences: A168069 A168070 A168071 * A168073 A168074 A168075

Keyword

easy,sign

Author

Paul Barry, Nov 18 2009

Extensions

Corrected by R. J. Mathar, Dec 03 2014

Status

approved