login
A129003
(n^3+n^2)*3^n.
1
6, 108, 972, 6480, 36450, 183708, 857304, 3779136, 15943230, 64953900, 257217444, 994857552, 3772168218, 14061928860, 51656065200, 187339329792, 671787127926, 2384960530284, 8391527791740, 29288988968400, 101486346775506
OFFSET
1,1
FORMULA
G.f.: 6x(1+6x)/(1-3x)^4. [From 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]
MATHEMATICA
LinearRecurrence[{12, -54, 108, -81}, {6, 108, 972, 6480}, 30] (* Vincenzo Librandi, Feb 12 2013 *)
PROG
(Magma) [(n^3+n^2)*3^n: n in [1..25]]; /* or */ 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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mohammad K. Azarian, May 01 2007
STATUS
approved