login
a(n) = (n^3+n)*9^n.
10

%I #27 Sep 08 2022 08:45:30

%S 0,18,810,21870,446148,7676370,117979902,1674039150,22384294920,

%T 285916320882,3521652245010,42113381995278,491427393476940,

%U 5617523480607090,63094193590782438,697970937800860110

%N a(n) = (n^3+n)*9^n.

%H Vincenzo Librandi, <a href="/A128074/b128074.txt">Table of n, a(n) for n = 0..1000</a> (corrected by Ray Chandler, Jan 19 2019)

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (36,-486,2916,-6561).

%F a(1)=18, a(2)=810, a(3)=21870, a(4)=446148, a(n)=36*a(n-1)- 486*a(n-2)+ 2916*a(n-3)-6561*a(n-4). - _Harvey P. Dale_, Jun 16 2011

%F G.f.: 18*x*(1+9*x+81*x^2)/(1-9*x)^4. - _Harvey P. Dale_, Jun 16 2011

%t Table[(n^3+n)9^n,{n,20}] (* or *) LinearRecurrence[{36,-486,2916,-6561}, {18,810,21870,446148},20] (* _Harvey P. Dale_, Jun 16 2011 *)

%o (Magma) [(n^3 + n) * 9^n: n in [1..20]]; // _Vincenzo Librandi_, Feb 22 2012

%o (PARI) A128074(n)=(n^3+n)*9^n \\ _M. F. Hasler_, Oct 06 2014

%Y Cf. A128796; A128960; A128985; A129002.

%K nonn,easy

%O 0,2

%A _Mohammad K. Azarian_, May 02 2007

%E Extended to a(0)=0 by _M. F. Hasler_, Oct 06 2014