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

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

Offset

1,1

Comments

a(n) has 5n-2 digits.

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

Links

Table of n, a(n) for n=1..8.

Index entries for linear recurrences with constant coefficients, signature (101101,-110201100,10110100000,-10000000000).

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

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A082521 A365994 A262645 * A292686 A138720 A262627

Adjacent sequences: A138823 A138824 A138825 * A138827 A138828 A138829

Keyword

base,easy,nonn

Author

Omar E. Pol, Apr 06 2008

Extensions

Corrected typo in exponent of my formula. - R. J. Mathar, Nov 09 2008

Status

approved