OFFSET
1,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Alice V. Kleeva, Grid for this sequence
Alice V. Kleeva, Illustration of initial terms
Robert Munafo, Sequence A169720, and two others by Alice V. Kleeva
Robert Munafo, Sequence A169720, and two others by Alice V. Kleeva [Cached copy, in pdf format, included with permission]
Index entries for linear recurrences with constant coefficients, signature (13,-39,27).
FORMULA
From R. J. Mathar, Apr 26 2010: (Start)
a(n) = 13*a(n-1) - 39*a(n-2) + 27*a(n-3).
G.f.: x*( -12 + 86*x - 90*x^2 ) / ( (x-1)*(3*x-1)*(9*x-1) ). (End)
E.g.f.: (2*exp(9*x) + 5*exp(3*x) + 3*exp(x) - 10)/3. - Stefano Spezia, Dec 25 2021
MAPLE
MATHEMATICA
Table[3^(n-1) (6 3^(n - 1) + 5) + 1, {n, 20}] (* or *) LinearRecurrence[{13, -39, 27}, {12, 70, 532}, 20] (* Harvey P. Dale, Aug 10 2011 *)
CoefficientList[Series[(-12 + 86 x - 90 x^2)/((x - 1) (3 x - 1) (9 x - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 03 2012 *)
PROG
(Magma) I:=[12, 70, 532]; [n le 3 select I[n] else 13*Self(n-1) -39*Self(n-2) +27*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Dec 03 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Alice V. Kleeva (alice27353(AT)gmail.com), Jan 19 2010
EXTENSIONS
G.f. adapted to the offset by Vincenzo Librandi, Dec 03 2012
STATUS
approved