login
a(n) = ((9*n + 8)*10^n - 8)/9.
3

%I #12 Oct 29 2017 13:34:34

%S 0,18,288,3888,48888,588888,6888888,78888888,888888888,9888888888,

%T 108888888888,1188888888888,12888888888888,138888888888888,

%U 1488888888888888,15888888888888888,168888888888888888,1788888888888888888,18888888888888888888,198888888888888888888

%N a(n) = ((9*n + 8)*10^n - 8)/9.

%H Colin Barker, <a href="/A294327/b294327.txt">Table of n, a(n) for n = 0..900</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,-120,100).

%F From _Colin Barker_, Oct 28 2017: (Start)

%F G.f.: 18*x*(1 - 5*x) / ((1 - x)*(1 - 10*x)^2).

%F a(n) = 21*a(n-1) - 120*a(n-2) + 100*a(n-3) for n>2.

%F (End)

%o (PARI) concat(0, Vec(18*x*(1 - 5*x) / ((1 - x)*(1 - 10*x)^2) + O(x^30))) \\ _Colin Barker_, Oct 28 2017

%Y Cf. A002282, A294328, A294329.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Oct 28 2017