A169725 a(n) = 3^(n-1)*(6*3^(n-1) + 5) + 1.

12, 70, 532, 4510, 39772, 355510, 3192292, 28708750, 258313132, 2324621350, 20921001652, 188287243390, 1694579876092, 15251202941590, 137260778644612, 1235346864312430, 11118121348344652, 100063090843700230, 900567813719097172, 8105110311849259870

Offset: 1

Author

Alice V. Kleeva (alice27353(AT)gmail.com), Jan 19 2010

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A169720-A169727, A100702.

Programs

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

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 *)

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

Extensions

G.f. adapted to the offset by Vincenzo Librandi, Dec 03 2012