OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (21,-147,343).
FORMULA
G.f.: 14*x/(1-7*x)^3. - Vincenzo Librandi, Feb 28 2013
a(n) = 21*a(n-1) - 147*a(n-2) + 343*a(n-3). - Vincenzo Librandi, Feb 28 2013
a(n+1) = 14*A027474(n+2). - Bruno Berselli, Feb 28 2013
E.g.f.: 7*x*(2 + 7*x)*exp(7*x). - G. C. Greubel, May 11 2019
From Amiram Eldar, Jul 20 2020: (Start)
Sum_{n>=1} 1/a(n) = 1 - 6*log(7/6).
Sum_{n>=1} (-1)^(n+1)/a(n) = 8*log(8/7) - 1. (End)
MATHEMATICA
Table[(n^2 + n) 7^n, {n, 0, 30}] (* Vincenzo Librandi, Feb 28 2013 *)
PROG
(Magma) [(n^2+n)*7^n: n in [0..30]]; // Vincenzo Librandi, Feb 28 2013
(Magma) I:=[0, 14, 294]; [n le 3 select I[n] else 21*Self(n-1)-147*Self(n-2)+343*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Feb 28 2013
(PARI) a(n)=(n^2+n)*7^n \\ Charles R Greathouse IV, Feb 28 2013
(Sage) [7^n*n*(n+1) for n in (0..30)] # G. C. Greubel, May 11 2019
(GAP) List([0..30], n-> 7^n*n*(n+1)); # G. C. Greubel, May 11 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mohammad K. Azarian, Apr 08 2007
STATUS
approved