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

Author

Omar E. Pol, Nov 11 2008

Keywords

• base
• easy
• nonn

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

Examples

			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 )
		

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).

Crossrefs

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

Programs

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

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 *)

PARI

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

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