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A138146 Palindromes with 2n-1 digits formed from the reflected decimal expansion of the concatenation of 1, 1, 1 and infinite 0's. 16
1, 111, 11111, 1110111, 111000111, 11100000111, 1110000000111, 111000000000111, 11100000000000111, 1110000000000000111, 111000000000000000111, 11100000000000000000111 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Bisection of A138145.

a(n) is also A147597(n) written in base 2. [Omar E. Pol, Nov 08 2008]

LINKS

Table of n, a(n) for n=1..12.

Index entries for linear recurrences with constant coefficients, signature (101,-100).

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)

EXAMPLE

n ............ a(n)

1 ............. 1

2 ............ 111

3 ........... 11111

4 .......... 1110111

5 ......... 111000111

6 ........ 11100000111

7 ....... 1110000000111

8 ...... 111000000000111

9 ..... 11100000000000111

10 ... 1110000000000000111

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 *)

PROG

(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

CROSSREFS

Cf. A138144, A138145.

Cf. A138118, A138119, A138120, A138721, A138826, A147597. [Omar E. Pol, Nov 08 2008]

Sequence in context: A267364 A265379 A265688 * A100706 A259102 A262629

Adjacent sequences:  A138143 A138144 A138145 * A138147 A138148 A138149

KEYWORD

easy,nonn,base

AUTHOR

Omar E. Pol, Mar 29 2008, May 18 2008

EXTENSIONS

Better definition from Omar E. Pol, Nov 16 2008

STATUS

approved

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Last modified April 23 07:51 EDT 2019. Contains 322381 sequences. (Running on oeis4.)