A141012 - OEIS

%I #26 Nov 13 2018 03:11:17

%S 0,2,14,170,2198,28562,371294,4826810,62748518,815730722,10604499374,

%T 137858491850,1792160394038,23298085122482,302875106592254,

%U 3937376385699290,51185893014090758

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

%H Vincenzo Librandi, <a href="/A141012/b141012.txt">Table of n, a(n) for n = 0..900</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14, -13).

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

%F From _R. J. Mathar_, Mar 05 2010: (Start)

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

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

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

%F a(n) = 13*a(n-1) - 12, n > 1. - _Vincenzo Librandi_, Sep 17 2011

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

%K nonn,easy

%O 0,2

%A _R. J. Mathar_, Jul 11 2008

%E Name changed by _Arkadiusz Wesolowski_, Sep 08 2013