A128961 a(n) = (n^3 - n)*3^n.

0, 54, 648, 4860, 29160, 153090, 734832, 3306744, 14171760, 58458510, 233834040, 911952756, 3482001432, 13057505370, 48212327520, 175630621680, 632270238048, 2252462723046, 7949868434280, 27824539519980, 96653663595720, 333455139405234, 1143274763675088

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (12,-54,108,-81).

Formula

G.f.: 54*x^2/(1-3*x)^4. - Vincenzo Librandi, Feb 12 2013

a(n) = 12*a(n-1) - 54*a(n-2) + 108*a(n-3) - 81*a(n-4). - Vincenzo Librandi, Feb 12 2013

From Amiram Eldar, Oct 02 2022: (Start)

a(n) = A007531(n+1)*A000244(n).

Sum_{n>=2} 1/a(n) = (2/3)*log(3/2) - 1/4.

Sum_{n>=2} (-1)^n/a(n) = (8/3)*log(4/3) - 3/4. (End)

Mathematica

LinearRecurrence[{12, -54, 108, -81}, {0, 54, 648, 4860}, 30] (* or *) CoefficientList[Series[54 x/(1 - 3 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 12 2013 *)

Prog

(Magma) [(n^3-n)*3^n: n in [1..25]]; /* or */ I:=[0, 54, 648, 4860]; [n le 4 select I[n] else 12*Self(n-1)-54*Self(n-2)+108*Self(n-3)-81*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Feb 12 2013

Crossrefs

Cf. A000244, A007531, A036289, A128796.

Cf. A128960, A128962, A128963, A128964, A128965, A128967, A128969.

Sequence in context: A086577 A193152 A253006 * A218130 A321635 A090835

Adjacent sequences: A128958 A128959 A128960 * A128962 A128963 A128964

Keyword

nonn,easy

Author

Mohammad K. Azarian, Apr 28 2007

Extensions

Offset corrected by Mohammad K. Azarian, Nov 20 2008

Status

approved