A155594 10^n+2^n-1.

1, 11, 103, 1007, 10015, 100031, 1000063, 10000127, 100000255, 1000000511, 10000001023, 100000002047, 1000000004095, 10000000008191, 100000000016383, 1000000000032767, 10000000000065535, 100000000000131071

Offset: 0

Author

Mohammad K. Azarian, Jan 24 2009

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (13,-32,20).

Crossrefs

Cf. A074501, A074600, A005057, A005056, A099393, A155588, A155590, A155592, A155593.

Programs

Mathematica

LinearRecurrence[{13,-32,20},{1,11,103},20] (* Harvey P. Dale, Mar 07 2015 *)

PARI

a(n)=10^n+2^n-1^n \\ Charles R Greathouse IV, Jun 11 2015

Formula

G.f.: 1/(1-10*x)+1/(1-2*x)-1/(1-x). E.g.f.: e^(10*x)+e^(2*x)-e^x.

a(n)=12*a(n-1)-20*a(n-2)-9 with a(0)=1, a(1)=11 - Vincenzo Librandi, Jul 21 2010

a(0)=1, a(1)=11, a(2)=103, a(n)=13*a(n-1)-32*a(n-2)+20*a(n-3). - Harvey P. Dale, Mar 07 2015

a(n) = A050621(n+1)-1. - R. J. Mathar, Mar 10 2022