A138145 -id:A138145 - cp's OEIS frontend

A147757 Palindromes formed from the reflected decimal expansion of the concatenation of 1, 0 and infinite digits 1.

1, 11, 101, 1001, 10101, 101101, 1011101, 10111101, 101111101, 1011111101, 10111111101, 101111111101, 1011111111101, 10111111111101, 101111111111101, 1011111111111101, 10111111111111101, 101111111111111101

Offset: 1

Omar E. Pol, Nov 11 2008

a(n) is also A147758(n) written in base 2.

a(A016789(n)) is divisible by 3 for n > 0. - Altug Alkan, Dec 06 2015

			n .... Successive digits of a(n)
1 ............. ( 1 )
2 ............ ( 1 1 )
3 ........... ( 1 0 1 )
4 .......... ( 1 0 0 1 )
5 ......... ( 1 0 1 0 1 )
6 ........ ( 1 0 1 1 0 1 )
7 ....... ( 1 0 1 1 1 0 1 )
8 ...... ( 1 0 1 1 1 1 0 1 )
9 ..... ( 1 0 1 1 1 1 1 0 1 )
10 ... ( 1 0 1 1 1 1 1 1 0 1 )

Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A000533, A016789, A135577, A138120, A138144, A138145, A138146, A138721, A138826, A147758.

Cf. A144564 (a bisection).

f[n_] := Block[{w = {1, 0}}, Which[n == 1, w = {1}, n == 2, w = {1, 1}, n == 3, AppendTo[w, 1], n >= 4, w = Join[w, Table[1, {n - 4}], Reverse@ w]]; FromDigits@ w]; Array[f, 19] (* Michael De Vlieger, Dec 05 2015 *)
LinearRecurrence[{11,-10},{1,11,101,1001,10101},20] (* Harvey P. Dale, Aug 02 2017 *)

Vec( x+11*x^2+101*x^3 -91*x^4*(-11+10*x) / ( (10*x-1)*(x-1) ) + O(x^30)) \\ Michel Marcus, Dec 05 2015

G.f.: x+11*x^2+101*x^3-91*x^4*(-11+10*x) / ( (10*x-1)*(x-1) ). - R. J. Mathar, Aug 24 2011

a(n) = 11*a(n-1) - 10*a(n-2) for n>2. Wesley Ivan Hurt, Dec 06 2015

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

cp's OEIS Frontend

A147757 Palindromes formed from the reflected decimal expansion of the concatenation of 1, 0 and infinite digits 1.

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