A144863 Start with 1, then at each step prepend 10 and append 01.

1, 10101, 101010101, 1010101010101, 10101010101010101, 101010101010101010101, 1010101010101010101010101, 10101010101010101010101010101, 101010101010101010101010101010101

Offset: 1

Author

Artur Jasinski, Sep 23 2008, Sep 25 2008

Keywords

• base
• nonn
• easy

Comments

Bisection of A094028. - Omar E. Pol, Nov 12 2008

a(n) is also A144864(n) written in base 2. - Omar E. Pol, Nov 13 2008

Quadrisection of A147759. - Omar E. Pol, Nov 16 2008

Links

• Index entries for linear recurrences with constant coefficients, signature (10001,-10000).

Crossrefs

Cf. A056830, A094028, A135576, A144864, A147759.

Programs

Mathematica

a = {}; k = {1}; Do[x = FromDigits[k, 2]; AppendTo[a, FromDigits[RealDigits[x, 2]]]; AppendTo[k, 0]; AppendTo[k, 1]; PrependTo[k, 0]; PrependTo[k, 1], {n, 1, 100}];
Table[FromDigits[RealDigits[1/12 (-4 + 16^n), 2]], {n, 1, 10}]
a = {}; k = 1; Do[AppendTo[a, k]; k = 10000 k + 101, {n, 1, 10}]; a
Table[1/99 (-1 + 100^(-1 + 2 n)), {n, 1, 20}]
LinearRecurrence[{10001,-10000},{1,10101},20] (* Harvey P. Dale, Aug 22 2014 *)

Formula

a(n) = (-1+100^(-1+2*n))/99.

If a(n) is interpreted as binary number, (-4+16^n)/12 gives the decimal representation of a(n).

a(n) = 10000*a(n-1)+101, n>1.

G.f.: x*(1+100*x) / ( (10000*x-1)*(x-1) ).