%I #19 Mar 08 2024 01:12:29

%S 1,1100,1110000,1111000000,1111100000000,1111110000000000,

%T 1111111000000000000,1111111100000000000000,1111111110000000000000000,

%U 1111111111000000000000000000,1111111111100000000000000000000,1111111111110000000000000000000000

%N Concatenation of n digits 1 and 2(n-1) digits 0.

%C a(n) is also A016152(n) written in base 2.

%H Paolo Xausa, <a href="/A147816/b147816.txt">Table of n, a(n) for n = 1..300</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1100,-100000).

%F a(n) = A138119(n)/10.

%F a(n) = 1100*a(n-1)-100000*a(n-2). G.f.: x / ((100*x-1)*(1000*x-1)). - _Colin Barker_, Sep 16 2013

%e n ...... a(n)

%e 1 ....... 1

%e 2 ...... 1100

%e 3 ..... 1110000

%e 4 .... 1111000000

%e 5 ... 1111100000000

%t Array[(10^#-1)*10^(2*#-2)/9 &, 20] (* or *)

%t LinearRecurrence[{1100, -100000}, {1, 1100}, 20] (* Paolo Xausa, Feb 27 2024 *)

%o (PARI) Vec(x/((100*x-1)*(1000*x-1)) + O(x^100)) \\ _Colin Barker_, Sep 16 2013

%Y Cf. A000533, A016152, A135577, A138119, A138120, A138144, A138145, A138146, A138721, A138826, A147757, A147759.

%K base,easy,nonn

%O 1,2

%A _Omar E. Pol_, Nov 13 2008