A369405 - OEIS

%I #45 Feb 27 2024 10:58:08

%S 100,110000,111000000,111100000000,111110000000000,111111000000000000,

%T 111111100000000000000,111111110000000000000000,

%U 111111111000000000000000000,111111111100000000000000000000,111111111110000000000000000000000,111111111111000000000000000000000000

%N Context-free language 1^n.0^(2n).

%C 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 Paolo Xausa, <a href="/A369405/b369405.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 From _Robert Israel_, Jan 22 2024: (Start)

%F a(n) = (10^n-1)*10^(2*n)/9.

%F G.f.: 100*x/(100000*x^2 - 1100*x + 1). (End)

%F From _Alois P. Heinz_, Feb 04 2024: (Start)

%F a(n) = A007088(A059409(n)).

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

%F a(n) = 100 * A147816(n). (End)

%p a:= n-> convert(4^n*(2^n-1), binary):

%p seq(a(n), n=1..15);  # _Alois P. Heinz_, Feb 04 2024

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

%t LinearRecurrence[{1100, -100000}, {100, 110000}, 20] (* _Paolo Xausa_, Feb 27 2024 *)

%o (Python)

%o def A369405(n): return (10**n-1)//9*10**(n<<1) # _Chai Wah Wu_, Feb 11 2024

%Y Cf. A007088, A059409, A138119, A147816.

%K nonn,easy

%O 1,1

%A _Vyom Narsana_, Jan 22 2024