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

0,2

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).

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

Mathematica

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

Prog

(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
(PARI) vector(20, n, n--; 8^n -1) \\ G. C. Greubel, Aug 03 2019
(Magma) [8^n -1: n in [0..20]]; // G. C. Greubel, Aug 03 2019
(GAP) List([0..30], n-> 8^n -1); # G. C. Greubel, Aug 03 2019

Crossrefs

Cf. A000225, A001576, A001018, A248725.

Sequence in context: A218633 A218283 A218237 * A291034 A155132 A270472

Adjacent sequences: A024085 A024086 A024087 * A024089 A024090 A024091

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved