A024102 a(n) = 9^n - n.

1, 8, 79, 726, 6557, 59044, 531435, 4782962, 43046713, 387420480, 3486784391, 31381059598, 282429536469, 2541865828316, 22876792454947, 205891132094634, 1853020188851825, 16677181699666552, 150094635296999103

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..400

Index entries for linear recurrences with constant coefficients, signature (11,-19,9).

Formula

G.f.: (1-3*x+10*x^2)/((1-9*x)(1-x)^2). - Vincenzo Librandi, Jun 17 2013

a(n) = 11*a(n-1)-19*a(n-2)+9*a(n-3). - Vincenzo Librandi, Jun 17 2013

Mathematica

Table[9^n - n, {n, 0, 20}] (* or *) CoefficientList[Series[(1 - 3 x + 10 x^2) / ((1 - 9 x) (1 - x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 17 2013 *)

Prog

(Magma) [9^n-n: n in [0..25]]; // Vincenzo Librandi, Jul 06 2011
(Magma) I:=[1, 8, 79]; [n le 3 select I[n] else 11*Self(n-1)-19*Self(n-2)+9*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 17 2013
(PARI) a(n)=9^n-n \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. numbers of the form k^n-n: A000325 (k=2), A024024 (k=3), A024037 (k=4), A024050 (k=5), A024063 (k=6), A024076 (k=7), A024089 (k=8), this sequence (k=9), A024115 (k=10), A024128 (k=11), A024141 (k=12).

Cf. A198966 (first differences).

Sequence in context: A160605 A353100 A224759 * A034355 A289213 A201513

Adjacent sequences: A024099 A024100 A024101 * A024103 A024104 A024105

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved