A199689 - OEIS

%I #22 Jun 30 2026 21:56:55

%S 9,81,801,8001,80001,800001,8000001,80000001,800000001,8000000001,

%T 80000000001,800000000001,8000000000001,80000000000001,

%U 800000000000001,8000000000000001,80000000000000001,800000000000000001,8000000000000000001,80000000000000000001,800000000000000000001

%N a(n) = 8*10^n + 1.

%H Vincenzo Librandi, <a href="/A199689/b199689.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) = 9*A059482(n).

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

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

%F G.f.: 9*(1-2*x)/((1-x)*(1-10*x)).

%F From _Elmo R. Oliveira_, May 04 2025: (Start)

%F E.g.f.: exp(x)*(1 + 8*exp(9*x)).

%F a(n) = 3*A199688(n). (End)

%t 8*10^Range[0,20]+1 (* _Harvey P. Dale_, Jun 11 2022 *)

%t (* Alternative: *)

%t LinearRecurrence[{11,-10},{9,81},20] (* _Harvey P. Dale_, Jun 11 2022 *)

%o (Magma) [8*10^n+1: n in [0..30]];

%Y Cf. A059482, A199688.

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, Nov 09 2011