login
a(n) = 4*10^n - 1.
1

%I #29 Sep 17 2024 15:41:21

%S 3,39,399,3999,39999,399999,3999999,39999999,399999999,3999999999,

%T 39999999999,399999999999,3999999999999,39999999999999,

%U 399999999999999,3999999999999999,39999999999999999,399999999999999999,3999999999999999999,39999999999999999999,399999999999999999999

%N a(n) = 4*10^n - 1.

%H Vincenzo Librandi, <a href="/A198970/b198970.txt">Table of n, a(n) for n = 0..200</a>

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

%F a(n) = 3*A097166(n).

%F a(n) = 10*a(n-1) + 9, n > 0.

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

%F G.f.: 3*(1 + 2*x)/(1 - 11*x + 10*x^2). - _Vincenzo Librandi_, Jan 03 2013

%F E.g.f.: exp(x)*(4*exp(9*x) - 1). - _Elmo R. Oliveira_, Sep 10 2024

%t CoefficientList[Series[3*(1 + 2*x)/(1 - 11*x + 10*x^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jan 03 2013 *)

%o (Magma) [4*10^n-1 : n in [0..20]];

%Y Cf. A097166.

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, Nov 01 2011