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,-54,108,-81).
FORMULA
G.f.: (1-2*x)/(1-3*x)^4.
a(n) = A006503(n+1)*3^(n-1).
a(n) = 12*a(n-1)-54*a(n-2)+108*a(n-3)-81*a(n-4). - Harvey P. Dale, Mar 21 2012
From G. C. Greubel, Dec 22 2023: (Start)
a(n) = (n+9)*A036068(n-1).
a(n) = A136158(n+3, 3).
E.g.f.: (1/2)*(2 + 14*x + 15*x^2 + 3*x^3)*exp(3*x). (End)
From Amiram Eldar, Jan 11 2024: (Start)
Sum_{n>=0} 1/a(n) = 44172*log(3/2)/7 - 20050659/7840.
Sum_{n>=0} (-1)^n/a(n) = 44496*log(4/3)/7 - 14329629/7840. (End)
MATHEMATICA
Table[((n+1)(n+2)(n+9)3^n)/18, {n, 0, 30}] (* or *) LinearRecurrence[ {12, -54, 108, -81}, {1, 10, 66, 360}, 30] (* Harvey P. Dale, Mar 21 2012 *)
CoefficientList[Series[(1 - 2 x) / (1 - 3 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 05 2013 *)
PROG
(Magma) [(n+1)*(n+2)*(n+9)*3^n/18: n in [0..30]]; // Vincenzo Librandi, Aug 05 2013
(SageMath) [(n+1)*(n+2)*(n+9)*3^(n-2)/2 for n in range(31)] # G. C. Greubel, Dec 22 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Feb 19 2003
STATUS
approved