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A147759 Palindromes formed from the reflected decimal expansion of the infinite concatenation of 1's and 0's. 7
1, 11, 101, 1001, 10101, 101101, 1010101, 10100101, 101010101, 1010110101, 10101010101, 101010010101, 1010101010101, 10101011010101, 101010101010101, 1010101001010101, 10101010101010101, 101010101101010101 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(k(n)) is divisible by 3 iff k(n) is defined by k(1) = 5 and k(n+1) - k(n) =  A100285(n+2). - Altug Alkan, Dec 05 2015

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (11,-20,110,-100).

FORMULA

a(n) = 11*a(n-1)-20*a(n-2)+110*a(n-3)-100*a(n-4). G.f.: x/((1-x)*(1-10*x)*(1+10*x^2)). [R. J. Mathar, Feb 20 2009]

EXAMPLE

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 0 1 0 1 )

8 ...... ( 1 0 1 0 0 1 0 1 )

9 ..... ( 1 0 1 0 1 0 1 0 1 )

10 ... ( 1 0 1 0 1 1 0 1 0 1 )

MATHEMATICA

CoefficientList[Series[1/((1 - x) (1 - 10 x) (1 + 10 x^2)), {x, 0, 20}], x] (* Vincenzo Librandi, Dec 05 2015 *)

PROG

(PARI) Vec(x/((1-x)*(1-10*x)*(1+10*x^2)) + O(x^30)) \\ Michel Marcus, Dec 05 2015

(MAGMA) I:=[1, 11, 101, 1001]; [n le 4 select I[n] else 11*Self(n-1)-20*Self(n-2)+110*Self(n-3)-100*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 05 2015

CROSSREFS

Cf. A000533, A094028, A135577, A138120, A138144, A138145, A138146, A138721, A138826, A147757.

Sequence in context: A116098 A116129 A000533 * A147757 A089183 A164046

Adjacent sequences:  A147756 A147757 A147758 * A147760 A147761 A147762

KEYWORD

base,easy,nonn

AUTHOR

Omar E. Pol, Nov 11 2008

STATUS

approved

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Last modified April 22 10:46 EDT 2019. Contains 322330 sequences. (Running on oeis4.)