OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (36,-486,2916,-6561).
FORMULA
From Harvey P. Dale, May 19 2011: (Start)
a(n) = 36*a(n-1)-486*a(n-2)+ 2916*a(n-3)-6561*a(n-4).
G.f.: 1/(1-9*x)^4. (End)
From Amiram Eldar, Aug 28 2022: (Start)
Sum_{n>=0} 1/a(n) = 1728*log(9/8) - 405/2.
Sum_{n>=0} (-1)^n/a(n) = 2700*log(10/9) - 567/2. (End)
MAPLE
MATHEMATICA
Table[Binomial[n + 3, 3]*9^n, {n, 0, 20}]
LinearRecurrence[{36, -486, 2916, -6561}, {1, 36, 810, 14580}, 30] (* Harvey P. Dale, May 19 2011 *)
PROG
(Magma) [Binomial(n+3, 3)*9^n: n in [0..20]]; // Vincenzo Librandi, Oct 13 2011
(PARI) a(n)=binomial(n+3, 3)*9^n \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Feb 12 2010
STATUS
approved