A129003 a(n) = (n^3 + n^2)*3^n.

6, 108, 972, 6480, 36450, 183708, 857304, 3779136, 15943230, 64953900, 257217444, 994857552, 3772168218, 14061928860, 51656065200, 187339329792, 671787127926, 2384960530284, 8391527791740, 29288988968400, 101486346775506

Offset: 1

Author

Mohammad K. Azarian, May 01 2007

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A036216, A128796, A036289.

Programs

Magma

[(n^3+n^2)*3^n: n in [1..25]]; // Vincenzo Librandi, Feb 12 2013

Magma

I:=[6,108,972,6480]; [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

Mathematica

LinearRecurrence[{12, -54, 108, -81}, {6, 108, 972, 6480}, 30] (* Vincenzo Librandi, Feb 12 2013 *)

Formula

G.f.: 6*x*(1+6*x)/(1-3*x)^4. - R. J. Mathar, Dec 19 2008

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

a(n) = 6*(A036216(n-1)+6*A036216(n-2)), with A036216(-1)=0. - Bruno Berselli, Feb 12 2013