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A169725
a(n) = 3^(n-1)*(6*3^(n-1) + 5) + 1.
1
12, 70, 532, 4510, 39772, 355510, 3192292, 28708750, 258313132, 2324621350, 20921001652, 188287243390, 1694579876092, 15251202941590, 137260778644612, 1235346864312430, 11118121348344652, 100063090843700230, 900567813719097172, 8105110311849259870
OFFSET
1,1
LINKS
Alice V. Kleeva, Grid for this sequence
Robert Munafo, Sequence A169720, and two others by Alice V. Kleeva [Cached copy, in pdf format, included with permission]
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
A169725 := proc(n)
3^(n-1)*(6*3^(n-1)+5)+1 ;
end proc: # R. J. Mathar, Jun 02 2016
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