A024076 a(n) = 7^n - n.

1, 6, 47, 340, 2397, 16802, 117643, 823536, 5764793, 40353598, 282475239, 1977326732, 13841287189, 96889010394, 678223072835, 4747561509928, 33232930569585, 232630513987190, 1628413597910431, 11398895185373124, 79792266297611981, 558545864083283986, 3909821048582988027

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (9,-15,7).

Crossrefs

Cf. numbers of the form k^n - n: A000325 (k=2), A024024 (k=3), A024037 (k=4), A024050 (k=5), A024063 (k=6), this sequence (k=7), A024089 (k=8), A024102 (k=9), A024115 (k=10), A024128 (k=11), A024141 (k=12).

Cf. A198688 (first differences).

Programs

Magma

[7^n-n: n in [0..25]]; // Vincenzo Librandi, Jul 03 2011

Magma

I:=[1, 6, 47]; [n le 3 select I[n] else 9*Self(n-1)-15*Self(n-2)+7*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 16 2013

Maple

A024076:=n->7^n-n; seq(A024076(n), n=0..30); # Wesley Ivan Hurt, Jan 24 2014

Mathematica

Table[7^n - n, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - 3 x + 8 x^2) / ((1 - 7 x) (1 - x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 16 2013 *)

PARI

a(n)=7^n-n \\ Charles R Greathouse IV, Oct 07 2015

Formula

From Vincenzo Librandi, Jun 16 2013: (Start)

G.f.: (1-3*x+8*x^2)/((1-7*x)*(1-x)^2).

a(n) = 9*a(n-1) - 15*a(n-2) + 7*a(n-3). (End)

E.g.f.: exp(x)*(exp(6*x) - x). - Elmo R. Oliveira, Sep 10 2024