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a(n) = 2^((n-1) mod 2)*5*10^floor((n-1)/2).
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%I #18 Sep 08 2022 08:46:15

%S 1,5,10,50,100,500,1000,5000,10000,50000,100000,500000,1000000,

%T 5000000,10000000,50000000,100000000,500000000,1000000000,5000000000,

%U 10000000000,50000000000,100000000000,500000000000,1000000000000,5000000000000,10000000000000

%N a(n) = 2^((n-1) mod 2)*5*10^floor((n-1)/2).

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,10).

%F G.f.: (1 + 5*x)/(1 - 10*x^2). - _Michael De Vlieger_, Jan 26 2016; amended by _Georg Fischer_, Apr 03 2019

%t Table[2^Mod[n-1, 2]*5*10^Floor[(n-1)/2], {n, 0, 30}] (* or *)

%t LinearRecurrence[{0, 10}, {1, 5, 10, 50}, 30] (* or *)

%t CoefficientList[Series[(1+5x)/(1-10 x^2), {x, 0, 30}], x] (* _Michael De Vlieger_, Jan 26 2016; amended for 1,5,... by _Georg Fischer_, Apr 03 2019 *)

%o (PARI) a(n)=2^((n-1)%2)*5*10^((n-1)\2) \\ _Georg Fischer_, Apr 03 2019

%o (Magma) I:=[1,5,10]; [n le 3 select I[n] else 10*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Jan 26 2016

%K nonn,easy

%O 0,2

%A _M. F. Hasler_, Jan 26 2016