A138146 Palindromes with 2n-1 digits formed from the reflected decimal expansion of the concatenation of 1, 1, 1 and infinite 0's.
1, 111, 11111, 1110111, 111000111, 11100000111, 1110000000111, 111000000000111, 11100000000000111, 1110000000000000111, 111000000000000000111, 11100000000000000000111
Offset: 1
Examples
n ............ a(n) 1 ............. 1 2 ............ 111 3 ........... 11111 4 .......... 1110111 5 ......... 111000111 6 ........ 11100000111 7 ....... 1110000000111 8 ...... 111000000000111 9 ..... 11100000000000111 10 ... 1110000000000000111
Links
- Index entries for linear recurrences with constant coefficients, signature (101,-100).
Crossrefs
Programs
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Mathematica
Table[FromDigits@ If[n < 4, ConstantArray[1, 2 n - 1], Join[#, ConstantArray[0, 2 n - 7], #]] &@ ConstantArray[1, 3], {n, 14}] (* or *) Rest@ CoefficientList[Series[-x (10 x - 1) (10 x + 1) (100 x^2 + 10 x + 1)/((x - 1) (100 x - 1)), {x, 0, 14}], x] (* Michael De Vlieger, Nov 25 2016 *) -
PARI
Vec(-x*(10*x-1)*(10*x+1)*(100*x^2+10*x+1)/((x-1)*(100*x-1)) + O(x^100)) \\ Colin Barker, Sep 16 2013
Formula
From Colin Barker, Sep 16 2013: (Start)
a(n) = 111 + 111*100^(n-2) for n>3.
a(n) = 101*a(n-1) - 100*a(n-2) for n>5.
G.f.: -x*(10*x-1)*(10*x+1)*(100*x^2+10*x+1) / ((x-1)*(100*x-1)). (End)
Extensions
Better definition from Omar E. Pol, Nov 16 2008
Comments