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A147757 Palindromes formed from the reflected decimal expansion of the concatenation of 1, 0 and infinite digits 1. 6
1, 11, 101, 1001, 10101, 101101, 1011101, 10111101, 101111101, 1011111101, 10111111101, 101111111101, 1011111111101, 10111111111101, 101111111111101, 1011111111111101, 10111111111111101, 101111111111111101 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is also A147758(n) written in base 2.

a(A016789(n)) is divisible by 3 for n > 0. - Altug Alkan, Dec 06 2015

LINKS

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

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

FORMULA

G.f.: x+11*x^2+101*x^3-91*x^4*(-11+10*x) / ( (10*x-1)*(x-1) ). - R. J. Mathar, Aug 24 2011

a(n) = 11*a(n-1) - 10*a(n-2) for n>2. Wesley Ivan Hurt, Dec 06 2015

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 1 1 0 1 )

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

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

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

MATHEMATICA

f[n_] := Block[{w = {1, 0}}, Which[n == 1, w = {1}, n == 2, w = {1, 1}, n == 3, AppendTo[w, 1], n >= 4, w = Join[w, Table[1, {n - 4}], Reverse@ w]]; FromDigits@ w]; Array[f, 19] (* Michael De Vlieger, Dec 05 2015 *)

LinearRecurrence[{11, -10}, {1, 11, 101, 1001, 10101}, 20] (* Harvey P. Dale, Aug 02 2017 *)

PROG

(PARI) Vec( x+11*x^2+101*x^3 -91*x^4*(-11+10*x) / ( (10*x-1)*(x-1) ) + O(x^30)) \\ Michel Marcus, Dec 05 2015

CROSSREFS

Cf. A000533, A016789, A135577, A138120, A138144, A138145, A138146, A138721, A138826, A147758.

Cf. A144564 (a bisection).

Sequence in context: A116129 A000533 A147759 * A089183 A164046 A284235

Adjacent sequences:  A147754 A147755 A147756 * A147758 A147759 A147760

KEYWORD

base,easy,nonn

AUTHOR

Omar E. Pol, Nov 11 2008

STATUS

approved

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Last modified May 27 02:54 EDT 2019. Contains 323597 sequences. (Running on oeis4.)