A138144 Palindromes formed from the reflected decimal expansion of the concatenation of 1, 1 and infinite 0's.

1, 11, 111, 1111, 11011, 110011, 1100011, 11000011, 110000011, 1100000011, 11000000011, 110000000011, 1100000000011, 11000000000011, 110000000000011, 1100000000000011, 11000000000000011, 110000000000000011

Offset

1,2

Comments

a(n) is also A147595(n) written in base 2. [From Omar E. Pol, Nov 08 2008]

Links

Table of n, a(n) for n=1..18.

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

Formula

a(n) = 11+11*10^(n-2) for n>3. a(n) = 11*a(n-1)-10*a(n-2). G.f.: -x*(10*x^2-1)*(10*x^2+1) / ((x-1)*(10*x-1)). - Colin Barker, Sep 15 2013

Example

n .... a(n)
1 .... 1
2 .... 11
3 .... 111
4 .... 1111
5 .... 11011
6 .... 110011
7 .... 1100011
8 .... 11000011
9 .... 110000011
10 ... 1100000011

Mathematica

LinearRecurrence[{11, -10}, {1, 11, 111, 1111, 11011}, 20] (* Harvey P. Dale, Aug 21 2016 *)

Prog

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

Crossrefs

Cf. A000533.

Cf. A138118, A138119, A138120, A138145, A138146, A138721, A138826, A147595. [From Omar E. Pol, Nov 08 2008]

Sequence in context: A283850 A283605 A083440 * A284243 A283005 A283256

Adjacent sequences: A138141 A138142 A138143 * A138145 A138146 A138147

Keyword

easy,nonn,base

Author

Omar E. Pol, Mar 29 2008

Extensions

Better definition. - Omar E. Pol, Nov 15 2008

Status

approved