OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (36,-486,2916,-6561).
FORMULA
From R. J. Mathar, Dec 19 2008 (Start)
G.f.: 486x^2/(1-9x)^4.
a(n) = 486*A038291(n+1,3). (End)
a(n) = 36*a(n-1) - 486*a(n-2) + 2916*a(n-3) - 6561*a(n-4). - Vincenzo Librandi, Feb 11 2013
From Amiram Eldar, Oct 02 2022: (Start)
Sum_{n>=2} 1/a(n) = (32/9)*log(9/8) - 5/12.
Sum_{n>=2} (-1)^n/a(n) = (50/9)*log(10/9) - 7/12. (End)
MATHEMATICA
CoefficientList[Series[486 x/(1 - 9 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 11 2013 *)
PROG
(Magma) [(n^3-n)*9^n: n in [0..25]]; (* or *) I:=[0, 486, 17496, 393660]; [n le 4 select I[n] else 36*Self(n-1) - 486*Self(n-2) + 2916*Self(n-3) - 6561*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Feb 11 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mohammad K. Azarian, Apr 28 2007
EXTENSIONS
Offset corrected by Mohammad K. Azarian, Nov 20 2008
STATUS
approved