A138826 Concatenation of 2n-1 digits 1, n digits 0 and 2n-1 digits 1.

101, 11100111, 1111100011111, 111111100001111111, 11111111100000111111111, 1111111111100000011111111111, 111111111111100000001111111111111, 11111111111111100000000111111111111111

Offset: 1

Author

Omar E. Pol, Apr 06 2008

Keywords

• base
• easy
• nonn

Comments

a(n) has 5n-2 digits.

a(n) is also A147540(n) written in base 2. [Omar E. Pol, Nov 08 2008]

Examples

			n ........... a(n)
1 ........... 101
2 ......... 11100111
3 ....... 1111100011111
4 ..... 111111100001111111
5 ... 11111111100000111111111
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..195
• Index entries for linear recurrences with constant coefficients, signature (101101,-110201100,10110100000,-10000000000).

Crossrefs

Cf. A138120, A138144, A138145, A138146, A138148, A138720, A138721, A138722, A147540.

Programs

Mathematica

Table[(1000^n + 10)*(100^n - 10)/900, {n, 10}] (* Paolo Xausa, Aug 08 2024 *)

PARI

Vec(x*(1100000000*x^3-2000000*x^2+888910*x+101)/((x-1)*(100*x-1)*(1000*x-1)*(100000*x-1)) + O(x^100)) \\ Colin Barker, Sep 16 2013

Formula

a(n) = (10^(2n-1)-1+10^(5n-2)-10^(3n-1))/9. [R. J. Mathar, Nov 07 2008, corrected Nov 09 2008]

G.f.: x*(1100000000*x^3-2000000*x^2+888910*x+101) / ((x-1)*(100*x-1)*(1000*x-1)*(100000*x-1)). - Colin Barker, Sep 16 2013