A213223 - OEIS

%I #22 Aug 29 2024 20:59:40

%S 1,20,120,1030,10040,100050,1000060,10000070,100000080,1000000090,

%T 10000000100,100000000110,1000000000120,10000000000130,

%U 100000000000140,1000000000000150,10000000000000160,100000000000000170,1000000000000000180,10000000000000000190,100000000000000000200

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

%H Vincenzo Librandi, <a href="/A213223/b213223.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12,-21,10).

%F G.f.: (1+8*x-99*x^2)/((1-x)^2*(1-10*x)).

%F a(n) = 12*a(n-1) - 21*a(n-2) + 10*a(n-3) for n > 2.

%F E.g.f.: exp(x)*(exp(9*x) + 10*x). - _Elmo R. Oliveira_, Aug 29 2024

%t Table[(10^n + 10 n), {n, 0, 30}] (* or *) CoefficientList[Series[(1 + 8 x - 99 x^2)/((1 - x)^2 (1 - 10 x)), {x, 0, 30}], x]

%o (Magma) [10^n + 10*n: n in [0..25]]; /* or */ I:=[1, 20, 120]; [n le 3 select I[n] else 12*Self(n-1)-21*Self(n-2)+10*Self(n-3): n in [1..30]];

%Y Cf. A198400.

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, Mar 03 2013