A024088 a(n) = 8^n - 1.

0, 7, 63, 511, 4095, 32767, 262143, 2097151, 16777215, 134217727, 1073741823, 8589934591, 68719476735, 549755813887, 4398046511103, 35184372088831, 281474976710655, 2251799813685247, 18014398509481983

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Numbers whose base 8 or octal representation is 777777.......7. - Zerinvary Lajos, Feb 03 2007

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-8).

Crossrefs

Cf. A000225, A001576, A001018, A248725.

Programs

GAP

List([0..30], n-> 8^n -1); # G. C. Greubel, Aug 03 2019

Magma

[8^n -1: n in [0..20]]; // G. C. Greubel, Aug 03 2019

Mathematica

8^Range[0,20]-1 (* or *) LinearRecurrence[{9,-8},{0,7},20] (* Harvey P. Dale, Jan 04 2017 *)

PARI

vector(20, n, n--; 8^n -1) \\ G. C. Greubel, Aug 03 2019

Sage

[gaussian_binomial(3*n,1,2) for n in range(0,20)] # Zerinvary Lajos, May 28 2009

Sage

[stirling_number2(3*n+1,2) for n in range(0,20)] # Zerinvary Lajos, Nov 26 2009

Sage

[8^n-1 for n in (0..20)] # Bruno Berselli, Nov 11 2015

Formula

From Mohammad K. Azarian, Jan 14 2009: (Start)

G.f.: 1/(1-8*x) - 1/(1-x).

E.g.f.: exp(8*x) - exp(x). (End)

a(n) = A000225(n)*A001576(n). - Reinhard Zumkeller, Feb 15 2009

a(n) = 8*a(n-1) + 7 for n>0, a(0)=0. - Vincenzo Librandi, Aug 03 2010

a(n) = Sum_{i=1..n} 7^i*binomial(n,n-i) for n>0, a(0)=0. - Bruno Berselli, Nov 11 2015

a(n) = A001018(n) - 1. - Sean A. Irvine, Jun 19 2019

Sum_{n>=1} 1/a(n) = A248725. - Amiram Eldar, Nov 13 2020