A024063 a(n) = 6^n - n.

1, 5, 34, 213, 1292, 7771, 46650, 279929, 1679608, 10077687, 60466166, 362797045, 2176782324, 13060694003, 78364164082, 470184984561, 2821109907440, 16926659444719, 101559956668398, 609359740010477, 3656158440062956, 21936950640377835, 131621703842267114, 789730223053602793

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (8,-13,6).

Formula

From Vincenzo Librandi, Jun 16 2013: (Start)

G.f.: (1-3*x+7*x^2)/((1-6*x)*(1-x)^2).

a(n) = 8*a(n-1) - 13*a(n-2) + 6*a(n-3). (End)

E.g.f.: exp(x)*(exp(5*x) - x). - Elmo R. Oliveira, Sep 10 2024

Mathematica

Table[6^n - n, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - 3 x + 7 x^2) / ((1 - 6 x) (1 - x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 16 2013 *)

Prog

(Magma) [6^n-n: n in [0..25]]; // Vincenzo Librandi, Jul 03 2011
(Magma) I:=[1, 5, 34]; [n le 3 select I[n] else 8*Self(n-1)-13*Self(n-2)+6*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 16 2013
(PARI) a(n)=6^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), this sequence (k=6), A024076 (k=7), A024089 (k=8), A024102 (k=9), A024115 (k=10), A024128 (k=11), A024141 (k=12).

Sequence in context: A076708 A353097 A127816 * A015545 A102436 A291027

Adjacent sequences: A024060 A024061 A024062 * A024064 A024065 A024066

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved