%I #18 Aug 09 2024 02:18:59

%S 1,11,111,1111,11111,111111,1110111,11100111,111000111,1110000111,

%T 11100000111,111000000111,1110000000111,11100000000111,

%U 111000000000111,1110000000000111,11100000000000111,111000000000000111

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

%C a(n) is also A147596(n) written in base 2. - _Omar E. Pol_, Nov 08 2008

%H Paolo Xausa, <a href="/A138145/b138145.txt">Table of n, a(n) for n = 1..995</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).

%F From _Colin Barker_, Sep 15 2013: (Start)

%F a(n) = 111+111*10^(n-3) for n>5.

%F a(n) = 11*a(n-1)-10*a(n-2).

%F G.f.: -x*(10*x^2-1)*(100*x^4+10*x^2+1) / ((x-1)*(10*x-1)). (End)

%e n .... a(n)

%e 1 .... 1

%e 2 .... 11

%e 3 .... 111

%e 4 .... 1111

%e 5 .... 11111

%e 6 .... 111111

%e 7 .... 1110111

%e 8 .... 11100111

%e 9 .... 111000111

%e 10 ... 1110000111

%e 11 ... 11100000111

%e 12 ... 111000000111

%e 13 ... 1110000000111

%t Table[If[n < 7, (10^n - 1)/9, 111 + 111*10^(n-3)], {n, 25}] (* or *)

%t LinearRecurrence[{11, -10}, {1, 11, 111, 1111, 11111, 111111, 1110111}, 25] (* _Paolo Xausa_, Aug 08 2024 *)

%o (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

%Y Cf. A000533, A138144.

%Y Cf. A138118, A138119, A138120, A138146, A138721, A138826, A147596. [From _Omar E. Pol_, Nov 08 2008]

%K easy,nonn,base

%O 1,2

%A _Omar E. Pol_, Mar 29 2008

%E Better definition from _Omar E. Pol_, Nov 16 2008