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A138145
Palindromes formed from the reflected decimal expansion of the concatenation of 1, 1, 1 and infinite 0's.
13
1, 11, 111, 1111, 11111, 111111, 1110111, 11100111, 111000111, 1110000111, 11100000111, 111000000111, 1110000000111, 11100000000111, 111000000000111, 1110000000000111, 11100000000000111, 111000000000000111
OFFSET
1,2
COMMENTS
a(n) is also A147596(n) written in base 2. - Omar E. Pol, Nov 08 2008
FORMULA
From Colin Barker, Sep 15 2013: (Start)
a(n) = 111+111*10^(n-3) for n>5.
a(n) = 11*a(n-1)-10*a(n-2).
G.f.: -x*(10*x^2-1)*(100*x^4+10*x^2+1) / ((x-1)*(10*x-1)). (End)
EXAMPLE
n .... a(n)
1 .... 1
2 .... 11
3 .... 111
4 .... 1111
5 .... 11111
6 .... 111111
7 .... 1110111
8 .... 11100111
9 .... 111000111
10 ... 1110000111
11 ... 11100000111
12 ... 111000000111
13 ... 1110000000111
MATHEMATICA
Table[If[n < 7, (10^n - 1)/9, 111 + 111*10^(n-3)], {n, 25}] (* or *)
LinearRecurrence[{11, -10}, {1, 11, 111, 1111, 11111, 111111, 1110111}, 25] (* Paolo Xausa, Aug 08 2024 *)
PROG
(PARI) Vec(-x*(10*x^2-1)*(100*x^4+10*x^2+1)/((x-1)*(10*x-1)) + O(x^100)) \\ Colin Barker, Sep 15 2013
CROSSREFS
KEYWORD
easy,nonn,base
AUTHOR
Omar E. Pol, Mar 29 2008
EXTENSIONS
Better definition from Omar E. Pol, Nov 16 2008
STATUS
approved