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
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..900
- Index entries for linear recurrences with constant coefficients, signature (14, -13).
Programs
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Mathematica
Join[{0},13^(#-1)+1&/@Range[20]] (* or *) Join[{0},LinearRecurrence[ {14,-13},{2,14},20]] (* Harvey P. Dale, Oct 14 2013 *)
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
Extensions
Name changed by Arkadiusz Wesolowski, Sep 08 2013