A138721 Concatenation of n digits 1, n digits 0 and n digits 1.

101, 110011, 111000111, 111100001111, 111110000011111, 111111000000111111, 111111100000001111111, 111111110000000011111111, 111111111000000000111111111, 111111111100000000001111111111, 111111111110000000000011111111111, 111111111111000000000000111111111111

Offset: 1

Author

Omar E. Pol, Mar 29 2008

Keywords

• nonn
• base
• easy

Comments

a(n) is also A145641(n) written in base 2. - Omar E. Pol, Oct 15 2008

a(n) has 3n digits. - Omar E. Pol, Nov 12 2008

Examples

			From _Omar E. Pol_, Nov 12 2008: (Start)
n         Successive digits of a(n)
1                 ( 1 0 1 )
2              ( 1 1 0 0 1 1 )
3           ( 1 1 1 0 0 0 1 1 1 )
4        ( 1 1 1 1 0 0 0 0 1 1 1 1 )
5     ( 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 )
(End)
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..300
• Index entries for linear recurrences with constant coefficients, signature (1111,-112110,1111000,-1000000).

Crossrefs

Cf. A000533, A135577, A138120, A138144, A138145, A138146, A138826, A145641, A147757, A147759.

Programs

Maple

a:= n-> parse(cat(1$n,0$n,1$n)):
seq(a(n), n=1..14);  # Alois P. Heinz, Mar 03 2022

Mathematica

Table[(100^n + 1)*(10^n - 1)/9, {n, 15}] (* Paolo Xausa, Aug 02 2024 *)

PARI

Vec(x*(101000*x^2-2200*x+101)/((x-1)*(10*x-1)*(100*x-1)*(1000*x-1)) + O(x^100)) \\ Colin Barker, Sep 16 2013

Formula

G.f.: x*(101000*x^2 - 2200*x + 101) / ((x-1)*(10*x-1)*(100*x-1)*(1000*x-1)). - Colin Barker, Sep 16 2013

a(n) = (100^n+1)*(10^n-1)/9. - Paolo Xausa, Aug 02 2024