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A138721 Concatenation of n digits 1, n digits 0 and n digits 1. 14
101, 110011, 111000111, 111100001111, 111110000011111, 111111000000111111, 111111100000001111111, 111111110000000011111111, 111111111000000000111111111, 111111111100000000001111111111 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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]

LINKS

Table of n, a(n) for n=1..10.

Index entries for linear recurrences with constant coefficients, signature (1111,-112110,1111000,-1000000).

FORMULA

a(n+1) = 1000*(a(n)-(10^n-1)/9)+10^(2*n+2)+(10^(n+1)-1)/9, with a(0)=101 and n>=1. - Paolo P. Lava, Apr 16 2008

a(n) = -(1/9)+(10/9)*10^n-(100/9)*100^n+(1000/9)*1000^n, with n>=0. [Paolo P. Lava, Oct 09 2008]

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]

EXAMPLE

Contribution 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)

MAPLE

P:=proc(n) local a, i; a:=101; print(a); for i from 1 by 1 to n do a:=(a-(10^i-1)/9)*1000+10^(2*i+2)+(10^(i+1)-1)/9; print(a); od; end: P(100); - Paolo P. Lava, Apr 16 2008

PROG

(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

CROSSREFS

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

Sequence in context: A261966 A076127 A180053 * A068659 A252491 A015078

Adjacent sequences:  A138718 A138719 A138720 * A138722 A138723 A138724

KEYWORD

nonn,base,easy

AUTHOR

Omar E. Pol, Mar 29 2008

STATUS

approved

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Last modified December 11 01:15 EST 2016. Contains 279033 sequences.