A138145 Palindromes formed from the reflected decimal expansion of the concatenation of 1, 1, 1 and infinite 0's.

1, 11, 111, 1111, 11111, 111111, 1110111, 11100111, 111000111, 1110000111, 11100000111, 111000000111, 1110000000111, 11100000000111, 111000000000111, 1110000000000111, 11100000000000111, 111000000000000111

Offset

1,2

Comments

a(n) is also A147596(n) written in base 2. - Omar E. Pol, Nov 08 2008

Links

Paolo Xausa, Table of n, a(n) for n = 1..995

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

Formula

From Colin Barker, Sep 15 2013: (Start)

a(n) = 111+111*10^(n-3) for n>5.

a(n) = 11*a(n-1)-10*a(n-2).

G.f.: -x*(10*x^2-1)*(100*x^4+10*x^2+1) / ((x-1)*(10*x-1)). (End)

Example

n .... a(n)
1 .... 1
2 .... 11
3 .... 111
4 .... 1111
5 .... 11111
6 .... 111111
7 .... 1110111
8 .... 11100111
9 .... 111000111
10 ... 1110000111
11 ... 11100000111
12 ... 111000000111
13 ... 1110000000111

Mathematica

Table[If[n < 7, (10^n - 1)/9, 111 + 111*10^(n-3)], {n, 25}] (* or *)
LinearRecurrence[{11, -10}, {1, 11, 111, 1111, 11111, 111111, 1110111}, 25] (* Paolo Xausa, Aug 08 2024 *)

Prog

(PARI) Vec(-x*(10*x^2-1)*(100*x^4+10*x^2+1)/((x-1)*(10*x-1)) + O(x^100)) \\ Colin Barker, Sep 15 2013

Crossrefs

Cf. A000533, A138144.

Cf. A138118, A138119, A138120, A138146, A138721, A138826, A147596. [From Omar E. Pol, Nov 08 2008]

Sequence in context: A090103 A061851 A247552 * A165370 A134962 A267257

Adjacent sequences: A138142 A138143 A138144 * A138146 A138147 A138148

Keyword

easy,nonn,base

Author

Omar E. Pol, Mar 29 2008

Extensions

Better definition from Omar E. Pol, Nov 16 2008

Status

approved