A024024 a(n) = 3^n - n.

1, 2, 7, 24, 77, 238, 723, 2180, 6553, 19674, 59039, 177136, 531429, 1594310, 4782955, 14348892, 43046705, 129140146, 387420471, 1162261448, 3486784381, 10460353182, 31381059587, 94143178804, 282429536457, 847288609418

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-7,3).

Formula

G.f.: (1-3*x+4*x^2)/((1-3*x)*(1-x)^2). - Vincenzo Librandi, Mar 06 2013

a(n) = 5*a(n-1) - 7*a(n-2) + 3*a(n-3). - Vincenzo Librandi, Mar 06 2013

Mathematica

Table[3^n - n, {n, 0, 40}] (* or *) CoefficientList[Series[(1 - 3 x + 4 x^2)/((1 - 3 x)(1 - x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Mar 06 2013 *)

Prog

(Magma) [3^n - n: n in [0..35]]; // Vincenzo Librandi, May 13 2011
(Magma) I:=[1, 2, 7]; [n le 3 select I[n] else 5*Self(n-1)-7*Self(n-2)+3*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Mar 06 2013
(PARI) a(n)=3^n-n \\ Charles R Greathouse IV, Sep 24 2015

Crossrefs

Cf. A000325, A024050.

Sequence in context: A341803 A272483 A129020 * A027122 A132788 A109682

Adjacent sequences: A024021 A024022 A024023 * A024025 A024026 A024027

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved