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
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
Programs
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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
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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
Comments