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

Author

Omar E. Pol, Mar 29 2008

Keywords

• easy
• nonn
• base

Comments

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

Examples

			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
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..995
• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Crossrefs

Cf. A000533, A138144.

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

Programs

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 *)

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

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)

Extensions

Better definition from Omar E. Pol, Nov 16 2008