A138144 - OEIS

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

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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