OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (12,-48,64).
FORMULA
From R. J. Mathar, Dec 19 2008: (Start)
G.f.: 8*x/(1-4*x)^3.
a(n) = 8*A038845(n-1). (End)
a(n) = 12*a(n-1) -48*a(n-2) +64*a(n-3). - Vincenzo Librandi, Feb 28 2013
E.g.f.: 8*x*(1 + 2*x)*exp(4*x). - G. C. Greubel, May 10 2019
From Amiram Eldar, Jul 20 2020: (Start)
Sum_{n>=1} 1/a(n) = 1 - 3*log(4/3).
Sum_{n>=1} (-1)^(n+1)/a(n) = 5*log(5/4) - 1. (End)
MATHEMATICA
Table[(n^2 + n)*4^n, {n, 0, 30}] (* Vincenzo Librandi, Feb 28 2013 *)
LinearRecurrence[{12, -48, 64}, {0, 8, 96}, 30] (* Harvey P. Dale, Feb 27 2015 *)
PROG
(Magma) [(n^2+n)*4^n: n in [0..30]]; // Vincenzo Librandi, Feb 28 2013
(Magma) I:=[0, 8, 96]; [n le 3 select I[n] else 12*Self(n-1)-48*Self(n-2)+64*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Feb 28 2013
(PARI) a(n)=(n^2+n)*4^n \\ Charles R Greathouse IV, Feb 28 2013
(SageMath) [4^n*n*(n+1) for n in (0..30)] # G. C. Greubel, May 10 2019
(GAP) List([0..30], n-> 4^n*n*(n+1)); # G. C. Greubel, May 10 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mohammad K. Azarian, Apr 08 2007
STATUS
approved