A138720 -id:A138720 - cp's OEIS frontend

A138120 Concatenation of n digits 1, 2n-1 digits 0 and n digits 1.

101, 1100011, 11100000111, 111100000001111, 1111100000000011111, 11111100000000000111111, 111111100000000000001111111, 1111111100000000000000011111111, 11111111100000000000000000111111111, 111111111100000000000000000001111111111

Offset: 1

Omar E. Pol, Apr 06 2008

a(n) has 4n-1 digits.

a(n) is also A147539(n) written in base 2. [Omar E. Pol, Nov 08 2008]

			n ........... a(n)
1 ........... 101
2 ......... 1100011
3 ....... 11100000111
4 ..... 111100000001111
5 ... 1111100000000011111

Index entries for linear recurrences with constant coefficients, signature (11011,-10121010,110110000,-100000000).

Cf. A138144, A138145, A138146, A138148, A138720, A138721, A138722, A138826.

Cf. A147539. [Omar E. Pol, Nov 08 2008]

a:= n-> parse(cat(1$n,0$(2*n-1),1$n)):
seq(a(n), n=1..11);  # Alois P. Heinz, Mar 03 2022

Table[FromDigits[Join[PadRight[{},n,1],PadRight[{},2n-1,0], PadRight[ {},n,1]]],{n,10}] (* or *) LinearRecurrence[{11011,-10121010,110110000,-100000000},{101,1100011,11100000111,111100000001111},10] (* Harvey P. Dale, Mar 19 2016 *)

Vec(x*(10001000*x^2-12100*x+101)/((x-1)*(10*x-1)*(1000*x-1)*(10000*x-1)) + O(x^100)) \\ Colin Barker, Sep 16 2013

def a(n): return int("1"*n + "0"*(2*n-1) + "1"*n)
print([a(n) for n in range(1, 11)]) # Michael S. Branicky, Mar 03 2022

G.f.: x*(10001000*x^2-12100*x+101) / ((x-1)*(10*x-1)*(1000*x-1)*(10000*x-1)). [Colin Barker, Sep 16 2013]

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

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Apr 06 2008

a(n) has 5n-2 digits.

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

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

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

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

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

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

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

A138119 Concatenation of n digits 1 and 2*n-1 digits 0.

Original entry on oeis.org

10, 11000, 11100000, 11110000000, 11111000000000, 11111100000000000, 11111110000000000000, 11111111000000000000000, 11111111100000000000000000, 11111111110000000000000000000, 11111111111000000000000000000000, 11111111111100000000000000000000000

Offset: 1

Omar E. Pol, Apr 03 2008

a(n) has 3*n-1 digits.

a(n) is also A147538(n) written in base 2. - Omar E. Pol, Nov 08 2008.

			n ...... a(n)
1 ....... 10
2 ...... 11000
3 ..... 11100000
4 .... 11110000000
5 ... 11111000000000

Index entries for linear recurrences with constant coefficients, signature (1100,-100000).

Cf. A138118, A138145, A138146, A138147, A138719, A138720, A138721, A138722, A147538.

LinearRecurrence[{1100, -100000}, {10, 11000}, 15] (* Paolo Xausa, Feb 06 2024 *)

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

From Colin Barker, Sep 16 2013: (Start)
a(n) = 1100*a(n-1) - 100000*a(n-2).
G.f.: 10*x / ((100*x-1)*(1000*x-1)). (End)

A138147 Concatenation of n digits 1 and n digits 0.

Original entry on oeis.org

10, 1100, 111000, 11110000, 1111100000, 111111000000, 11111110000000, 1111111100000000, 111111111000000000, 11111111110000000000, 1111111111100000000000, 111111111111000000000000, 11111111111110000000000000, 1111111111111100000000000000, 111111111111111000000000000000

Offset: 1

Omar E. Pol, Mar 29 2008

Also, a(n) = binary representation of A020522(n), for n>0 (see example).

			n ... A020522(n) ..... a(n)
1 ....... 2 ........... 10
2 ...... 12 .......... 1100
3 ...... 56 ......... 111000
4 ..... 240 ........ 11110000
5 ..... 992 ....... 1111100000
6 .... 4032 ...... 111111000000
7 ... 16256 ..... 11111110000000

J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 136, Ex. 4.2.2. - N. J. A. Sloane, Jul 27 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..95
Index entries for linear recurrences with constant coefficients, signature (110,-1000).

Cf. A002275, A020522, A138144, A138145, A138720, A276352.

Cf. A109241, A138118, A138119, A138120, A138146, A138721, A138826. - Omar E. Pol, Nov 08 2008

[(10^(2*n) - 10^n)/9: n in [1..30]]; // Vincenzo Librandi, Apr 26 2011

Table[FromDigits[Join[PadRight[{},n,1],PadRight[{},n,0]]],{n,15}] (* Harvey P. Dale, Nov 20 2011 *)

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

a(n) = (10^(2*n) - 10^n)/9 = A002275(n)*10^n. - Omar E. Pol, Apr 16 2008
a(n) = 10*A109241(n-1). - Omar E. Pol, Nov 08 2008
From Colin Barker, Sep 16 2013: (Start)
a(n) = 110*a(n-1) - 1000*a(n-2).
G.f.: 10*x/((10*x-1)*(100*x-1)). (End)
From Elmo R. Oliveira, Jun 13 2025: (Start)
E.g.f.: exp(10*x)*(exp(90*x) - 1)/9.
a(n) = A276352(n)/9. (End)

cp's OEIS Frontend

A138120 Concatenation of n digits 1, 2n-1 digits 0 and n digits 1.

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

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A138119 Concatenation of n digits 1 and 2*n-1 digits 0.

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A138147 Concatenation of n digits 1 and n digits 0.

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