A141012 a(0) = 0, a(n) = 13^(n-1) + 1.

0, 2, 14, 170, 2198, 28562, 371294, 4826810, 62748518, 815730722, 10604499374, 137858491850, 1792160394038, 23298085122482, 302875106592254, 3937376385699290, 51185893014090758

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..900

Index entries for linear recurrences with constant coefficients, signature (14, -13).

Formula

E.g.f.: Sum_{d|M} (exp(d*x) - 1)/d, M=13.

From R. J. Mathar, Mar 05 2010: (Start)

a(n) = Sum_{d|13} d^(n-1) = 1 + 13^(n-1) = 1 + A001022(n-1), n > 0.

a(n) = 14*a(n-1) - 13*a(n-2), n > 2.

G.f.: -2*x*(-1+7*x)/((13*x-1)*(x-1)). (End)

a(n) = 13*a(n-1) - 12, n > 1. - Vincenzo Librandi, Sep 17 2011

Mathematica

Join[{0}, 13^(#-1)+1&/@Range[20]] (* or *) Join[{0}, LinearRecurrence[ {14, -13}, {2, 14}, 20]] (* Harvey P. Dale, Oct 14 2013 *)

Crossrefs

Sequence in context: A229257 A188194 A046247 * A351277 A235369 A380040

Adjacent sequences: A141009 A141010 A141011 * A141013 A141014 A141015

Keyword

nonn,easy

Author

R. J. Mathar, Jul 11 2008

Extensions

Name changed by Arkadiusz Wesolowski, Sep 08 2013

Status

approved