A138120 -id:A138120 - cp's OEIS frontend

A152756 Bisection of A000533.

1, 101, 10001, 1000001, 100000001, 10000000001, 1000000000001, 100000000000001, 10000000000000001, 1000000000000000001, 100000000000000000001, 10000000000000000000001

Offset: 1

Omar E. Pol, Dec 13 2008

a(1)=1, for n>1, a(n) is the concatenation of "1", 2(n-1)-1 digits "0" and "1". - Omar E. Pol, Dec 14 2008

			n ..... a(n)
1 ....... 1
2 ...... 101
3 ..... 10001
4 .... 1000001
5 ... 100000001

Index entries for linear recurrences with constant coefficients, signature (101,-100).

Cf. A000533, A135577, A138120, A138146.

[1] cat [10^(2*n)+1: n in [1..15]]; // Vincenzo Librandi, Jul 27 2014

A152756[n_] := If[n == 1, 1, 100^(n-1) + 1]; Array[A152756, 20] (* or *)
LinearRecurrence[{101, -100}, {1, 101, 10001}, 20] (* Paolo Xausa, Oct 05 2024 *)

Except the first term, a(n)=10^(2n-2)+1. - Robert G. Wilson v, Dec 14 2008

G.f.: x*(1-100*x^2)/(1-x)/(1-100*x). - Robert Israel, Jul 27 2014

A147816 Concatenation of n digits 1 and 2(n-1) digits 0.

Original entry on oeis.org

1, 1100, 1110000, 1111000000, 1111100000000, 1111110000000000, 1111111000000000000, 1111111100000000000000, 1111111110000000000000000, 1111111111000000000000000000, 1111111111100000000000000000000, 1111111111110000000000000000000000

Offset: 1

Omar E. Pol, Nov 13 2008

a(n) is also A016152(n) written in base 2.

			n ...... a(n)
1 ....... 1
2 ...... 1100
3 ..... 1110000
4 .... 1111000000
5 ... 1111100000000

Paolo Xausa, Table of n, a(n) for n = 1..300
Index entries for linear recurrences with constant coefficients, signature (1100,-100000).

Cf. A000533, A016152, A135577, A138119, A138120, A138144, A138145, A138146, A138721, A138826, A147757, A147759.

Array[(10^#-1)*10^(2*#-2)/9 &, 20] (* or *)
LinearRecurrence[{1100, -100000}, {1, 1100}, 20] (* Paolo Xausa, Feb 27 2024 *)

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

a(n) = A138119(n)/10.

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

A144564 Bisection of A147757.

Original entry on oeis.org

1, 101, 10101, 1011101, 101111101, 10111111101, 1011111111101, 101111111111101, 10111111111111101, 1011111111111111101, 101111111111111111101, 10111111111111111111101, 1011111111111111111111101, 101111111111111111111111101, 10111111111111111111111111101

Offset: 1

Omar E. Pol, Dec 14 2008

			n ...... a(n)
1 ....... 1
2 ...... 101
3 ..... 10101
4 .... 1011101
5 ... 101111101

Index entries for linear recurrences with constant coefficients, signature (101,-100).

Cf. A135577, A138120, A138146, A147757, A152756.

Rest[CoefficientList[Series[x(1+10x)(100x^2-10x+1)/((100x-1)(x-1)),{x,0,20}],x]] (* or *) Join[{1,101},Table[FromDigits[Join[{1,0},PadRight[ {},2n+1,1],{0,1}]],{n,0,20}]] (* Harvey P. Dale, Dec 26 2014 *)

G.f.: x*(1+10*x)*(100*x^2-10*x+1)/((100*x-1)*(x-1)). - R. J. Mathar, Aug 24 2011

A152764 Bisection of A138144.

Original entry on oeis.org

1, 111, 11011, 1100011, 110000011, 11000000011, 1100000000011, 110000000000011, 11000000000000011, 1100000000000000011, 110000000000000000011, 11000000000000000000011

Offset: 1

Omar E. Pol, Dec 14 2008

			n ...... a(n)
1 ....... 1
2 ...... 111
3 ..... 11011
4 .... 1100011
5 ... 110000011

Index entries for linear recurrences with constant coefficients, signature (101,-100).

Cf. A135577, A138120, A138146, A152756, A152758, A058764.

LinearRecurrence[{101,-100},{1,111,11011,1100011},20] (* Harvey P. Dale, Nov 26 2019 *)

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

From Colin Barker, Sep 16 2013: (Start)
a(n) = 11+11*10^(2*n-3) for n>2.
a(n) = 101*a(n-1)-100*a(n-2) for n>4.
G.f.: -x*(10*x-1)*(10*x+1)^2 / ((x-1)*(100*x-1)). (End)

A147818 Period 4: repeat [5, 9, 9, 5].

Original entry on oeis.org

5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5

Offset: 1

Omar E. Pol, Nov 14 2008, Jan 25 2009

Last digit of the number whose binary representation is the concatenation of n 1's, 2n-1 0's and n 1's.

a(n) is the final digit of A147539(n).

Index entries for linear recurrences with constant coefficients, signature (1,-1,1).

Cf. A138120, A147539.

&cat [[5, 9, 9, 5]^^30]; // Wesley Ivan Hurt, Jul 09 2016

A010879 := proc(n) n mod 10; end:
A147539 := proc(n) 2^n-1+2^(4*n-1)-2^(3*n-1); end:
A147818 := proc(n) A010879(A147539(n)); end: # R. J. Mathar, Jan 22 2009
seq(op([5, 9, 9, 5]), n=1..40); # Wesley Ivan Hurt, Jul 09 2016

PadRight[{}, 100, {5, 9, 9, 5}] (* Wesley Ivan Hurt, Jul 09 2016 *)

a(n+1) = 7-2*cos(Pi*n/2)+2*sin(Pi*n/2). - R. J. Mathar, Oct 08 2011
a(n) = a(n-1)-a(n-2)+a(n-3) for n>3. G.f.: x*(5*x^2+4*x+5)/((1-x)*(x^2+1)). [Colin Barker, Nov 04 2012]
a(n) = a(n-4) for n>4. - Wesley Ivan Hurt, Jul 09 2016

More terms from R. J. Mathar, Jan 22 2009

cp's OEIS Frontend

A152756 Bisection of A000533.

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A147816 Concatenation of n digits 1 and 2(n-1) digits 0.

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A144564 Bisection of A147757.

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A152764 Bisection of A138144.

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A147818 Period 4: repeat [5, 9, 9, 5].

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