A129004 a(n) = (n^3 + n^2)*4^n.

8, 192, 2304, 20480, 153600, 1032192, 6422528, 37748736, 212336640, 1153433600, 6090129408, 31406948352, 158779572224, 789200240640, 3865470566400, 18691697672192, 89369679495168, 423037098786816, 1984618488135680, 9235897673318400, 42669847250731008, 195836215046438912

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 (16,-96,256,-256).

Crossrefs

Cf. A036289, A038846, A128796.

Programs

Magma

[(n^3+n^2)*4^n: n in [1..25]]; // Vincenzo Librandi, Feb 12 2013

Mathematica

Table[(n^3+n^2)4^n,{n, 20}] (* or *) LinearRecurrence[{16,-96,256,-256}, {8,192,2304,20480},20] (* Harvey P. Dale, May 12 2011 *)

Formula

G.f.: 8*x*(1+8*x)/(1-4*x)^4. - R. J. Mathar, Dec 19 2008

a(1)=8, a(2)=192, a(3)=2304, a(4)=20480, a(n)=16*a(n-1)-96*a(n-2)+ 256*a(n-3)-256*a(n-4). - Harvey P. Dale, May 12 2011

a(n) = 8*(A038846(n-1)+8*A038846(n-2)), with A038846(-1)=0. - Bruno Berselli, Feb 12 2013

E.g.f.: 8*exp(4*x)*x*(1 + 8*x + 8*x^2). - Stefano Spezia, Sep 02 2024