A147759 Palindromes formed from the reflected decimal expansion of the infinite concatenation of 1's and 0's.

1, 11, 101, 1001, 10101, 101101, 1010101, 10100101, 101010101, 1010110101, 10101010101, 101010010101, 1010101010101, 10101011010101, 101010101010101, 1010101001010101, 10101010101010101, 101010101101010101

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

Matthew Schulz, Table of n, a(n) for n = 1..1000

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

Formula

From R. J. Mathar, Feb 20 2009: (Start)

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)). (End)

E.g.f.: (exp(x)*(10*exp(9*x) - 1) - 9*cos(sqrt(10)*x))/99. - Stefano Spezia, Oct 12 2024

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[x/((1 - x) (1 - 10 x) (1 + 10 x^2)), {x, 0, 20}], x] (* Vincenzo Librandi, Dec 05 2015 *)
LinearRecurrence[{11, -20, 110, -100}, {1, 11, 101, 1001}, 30] (* Harvey P. Dale, Apr 10 2022 *)

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: A116129 A056810 A000533 * A147757 A089183 A384979

Adjacent sequences: A147756 A147757 A147758 * A147760 A147761 A147762

Keyword

base,easy,nonn

Author

Omar E. Pol, Nov 11 2008

Status

approved