A024089 a(n) = 8^n - n.

1, 7, 62, 509, 4092, 32763, 262138, 2097145, 16777208, 134217719, 1073741814, 8589934581, 68719476724, 549755813875, 4398046511090, 35184372088817, 281474976710640, 2251799813685231, 18014398509481966, 144115188075855853, 1152921504606846956, 9223372036854775787

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (10,-17,8).

Formula

From Vincenzo Librandi, Jun 17 2013: (Start)

G.f.: (1-3*x+9*x^2)/((1-8*x)*(1-x)^2).

a(n) = 10*a(n-1) - 17*a(n-2) + 8*a(n-3). (End)

E.g.f.: exp(x)*(exp(7*x) - x). - Elmo R. Oliveira, Sep 10 2024

Mathematica

Table[8^n - n, {n, 0, 20}] (* or *) CoefficientList[Series[(1 - 3 x + 9 x^2) / ((1 - 8 x) (1 - x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 17 2013 *)
LinearRecurrence[{10, -17, 8}, {1, 7, 62}, 30] (* Harvey P. Dale, Sep 28 2017 *)

Prog

(Magma) [8^n-n: n in [0..20]]; // Vincenzo Librandi, Jul 05 2011
(Magma) I:=[1, 7, 62]; [n le 3 select I[n] else 10*Self(n-1)-17*Self(n-2)+8*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 17 2013
(PARI) a(n)=8^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), this sequence (k=8), A024102 (k=9), A024115 (k=10), A024128 (k=11), A024141 (k=12).

Cf. A198855 (first differences).

Sequence in context: A368057 A180776 A353099 * A327588 A287481 A289212

Adjacent sequences: A024086 A024087 A024088 * A024090 A024091 A024092

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved