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A144564 Bisection of A147757. 3
1, 101, 10101, 1011101, 101111101, 10111111101, 1011111111101, 101111111111101, 10111111111111101, 1011111111111111101, 101111111111111111101, 10111111111111111111101 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

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

FORMULA

a(n)=-(91/9)+(91000/9)*100^(n-3)+(101/10)*{C[2*(n-1),(n-1)] mod 2}+10*{C[2*(n-2),n-2] mod 2}, with n>=1 [From Paolo P. Lava, Dec 22 2008]

G.f. x*(1+10*x)*(100*x^2-10*x+1)/( (100*x-1)*(x-1)) .- R. J. Mathar, Aug 24 2011

EXAMPLE

n ...... a(n)

1 ....... 1

2 ...... 101

3 ..... 10101

4 .... 1011101

5 ... 101111101

MATHEMATICA

Rest[CoefficientList[Series[x(1+10x)(100x^2-10x+1)/((100x-1)(x-1)), {x, 0, 20}], x]] (* or *) Join[{1, 101}, Table[FromDigits[Join[{1, 0}, PadRight[ {}, 2n+1, 1], {0, 1}]], {n, 0, 20}]] (* Harvey P. Dale, Dec 26 2014 *)

CROSSREFS

Cf. A135577, A138120, A138146, A147757, A152756.

Sequence in context: A164367 A263244 A094028 * A261965 A255892 A065074

Adjacent sequences:  A144561 A144562 A144563 * A144565 A144566 A144567

KEYWORD

easy,nonn,base

AUTHOR

Omar E. Pol, Dec 14 2008

STATUS

approved

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Last modified April 24 09:54 EDT 2019. Contains 322420 sequences. (Running on oeis4.)