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a(1)=10; a(n)=a(n-1)*10 -/+ 1 (alternating)
1

%I #18 Mar 04 2024 01:15:18

%S 10,99,991,9909,99091,990909,9909091,99090909,990909091,9909090909,

%T 99090909091,990909090909,9909090909091,99090909090909,

%U 990909090909091,9909090909090909,99090909090909091,990909090909090909,9909090909090909091,99090909090909090909

%N a(1)=10; a(n)=a(n-1)*10 -/+ 1 (alternating)

%C 109/110 = 0,9909090909....

%H Vincenzo Librandi, <a href="/A179557/b179557.txt">Table of n, a(n) for n = 1..100</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (9, 10).

%F a(1)=10, a(2)=99, a(n)=9*a(n-1)+10*a(n-2). - _Harvey P. Dale_, Jul 21 2014

%t nxt[{a_,i_}]:={10a+i,-i}; Transpose[NestList[nxt,{10,-1},30]][[1]] (* or *) LinearRecurrence[{9,10},{10,99},30] (* _Harvey P. Dale_, Jul 21 2014 *)

%o (Magma) [(1/11)*((-1)^(n-1)+109*10^(n-1)): n in [1..20]]; // _Vincenzo Librandi_, Jul 21 2014

%K nonn,easy

%O 1,1

%A _Mark Dols_, Jul 19 2010