login
a(n) = 5*10^n + 1.
6

%I #21 Sep 16 2024 03:11:05

%S 6,51,501,5001,50001,500001,5000001,50000001,500000001,5000000001,

%T 50000000001,500000000001,5000000000001,50000000000001,

%U 500000000000001,5000000000000001,50000000000000001,500000000000000001,5000000000000000001,50000000000000000001,500000000000000000001

%N a(n) = 5*10^n + 1.

%H Vincenzo Librandi, <a href="/A199685/b199685.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).

%F a(n) = 3*A126109(n).

%F a(n) = 10*a(n-1) - 9.

%F a(n) = 11*a(n-1) - 10*a(n-2).

%F G.f.: 3*(2-5*x)/((1-x)*(1-10*x)).

%F E.g.f.: exp(x)*(5*exp(9*x) + 1). - _Elmo R. Oliveira_, Sep 15 2024

%t LinearRecurrence[{11,-10},{6,51},30] (* _Harvey P. Dale_, Apr 06 2013 *)

%o (Magma) [5*10^n+1: n in [0..30]];

%o (PARI) a(n)=5*10^n+1 \\ _Charles R Greathouse IV_, Oct 16 2015

%Y Cf. A126109.

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, Nov 09 2011