OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (27,-243,729).
FORMULA
G.f.: 18*x/(1-9*x)^3. - Vincenzo Librandi, Feb 28 2013
a(n) = 27*a(n-1) - 243*a(n-2) + 729*a(n-3). - Vincenzo Librandi, Feb 28 2013
a(n) = 18*A081139(n+1). - Bruno Berselli, Mar 01 2013
E.g.f.: 9*x*(2 + 9*x)*exp(9*x). - G. C. Greubel, May 11 2019
From Amiram Eldar, Jul 20 2020: (Start)
Sum_{n>=1} 1/a(n) = 1 - 8*log(9/8).
Sum_{n>=1} (-1)^(n+1)/a(n) = 10*log(10/9) - 1. (End)
MATHEMATICA
Table[(n^2 + n) 9^n, {n, 0, 20}] (* Vincenzo Librandi, Feb 28 2013 *)
PROG
(Magma) [(n^2+n)*9^n: n in [0..20]]; // Vincenzo Librandi, Feb 28 2013
(PARI) {a(n) = 9^n*n*(n+1)}; \\ G. C. Greubel, May 11 2019
(Sage) [9^n*n*(n+1) for n in (0..20)] # G. C. Greubel, May 11 2019
(GAP) List([0..20], n-> 9^n*n*(n+1)) # G. C. Greubel, May 11 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mohammad K. Azarian, Apr 08 2007
STATUS
approved