A103459 a(n) = 8^n + 1 - 0^n.

1, 9, 65, 513, 4097, 32769, 262145, 2097153, 16777217, 134217729, 1073741825, 8589934593, 68719476737, 549755813889, 4398046511105, 35184372088833, 281474976710657, 2251799813685249, 18014398509481985, 144115188075855873

Offset: 0

Author

Paul Barry, Feb 07 2005

Keywords

• easy
• nonn

Comments

a(n)^3 is palindromic in base 8 (1_8, 1331_8, 1030301_8, 1003003001_8, ...).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Patrick De Geest, World!Of Numbers
• Index entries for linear recurrences with constant coefficients, signature (9,-8).

Crossrefs

Cf. A046233, A062395.

Programs

Magma

[1] cat [8^n + 1: n in [1..30]]; // G. C. Greubel, Jun 23 2021

Mathematica

Join[{1},8^Range[20]+1] (* or *) Join[{1},LinearRecurrence[{9,-8},{9,65},20]] (* Harvey P. Dale, Oct 21 2011 *)

Sage

[1]+[8^n+1 for n in (1..30)] # G. C. Greubel, Jun 23 2021

Formula

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

a(n) = Sum_{k=0..n} binomial(n, k)*0^(k(n-k))*8^k.

a(n) = A062395(n), n > 0. - R. J. Mathar, Aug 28 2008

a(n) = 8*a(n-1) - 7, with a(1)=9. - Vincenzo Librandi, Dec 29 2010

a(n) = 9*a(n-1) - 8*a(n-2); a(0)=1, a(1)=9, a(2)=65. - Harvey P. Dale, Oct 21 2011

E.g.f.: -1 + exp(x) + exp(8*x). - G. C. Greubel, Jun 23 2021