This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A369405 #45 Feb 27 2024 10:58:08
%S A369405 100,110000,111000000,111100000000,111110000000000,111111000000000000,
%T A369405 111111100000000000000,111111110000000000000000,
%U A369405 111111111000000000000000000,111111111100000000000000000000,111111111110000000000000000000000,111111111111000000000000000000000000
%N A369405 Context-free language 1^n.0^(2n).
%C A369405 This sequence represents the context-free language 1^n.0^(2n) which can be accepted by a pushdown automaton. It finds applications in the study of formal languages and automata theory in theoretical computer science.
%H A369405 Paolo Xausa, <a href="/A369405/b369405.txt">Table of n, a(n) for n = 1..300</a>
%H A369405 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1100,-100000).
%F A369405 From _Robert Israel_, Jan 22 2024: (Start)
%F A369405 a(n) = (10^n-1)*10^(2*n)/9.
%F A369405 G.f.: 100*x/(100000*x^2 - 1100*x + 1). (End)
%F A369405 From _Alois P. Heinz_, Feb 04 2024: (Start)
%F A369405 a(n) = A007088(A059409(n)).
%F A369405 a(n) = 10 * A138119(n).
%F A369405 a(n) = 100 * A147816(n). (End)
%p A369405 a:= n-> convert(4^n*(2^n-1), binary):
%p A369405 seq(a(n), n=1..15); # _Alois P. Heinz_, Feb 04 2024
%t A369405 Array[(10^#-1)*10^(2*#)/9 &, 20] (* or *)
%t A369405 LinearRecurrence[{1100, -100000}, {100, 110000}, 20] (* _Paolo Xausa_, Feb 27 2024 *)
%o A369405 (Python)
%o A369405 def A369405(n): return (10**n-1)//9*10**(n<<1) # _Chai Wah Wu_, Feb 11 2024
%Y A369405 Cf. A007088, A059409, A138119, A147816.
%K A369405 nonn,easy
%O A369405 1,1
%A A369405 _Vyom Narsana_, Jan 22 2024