A164367 a(n) = A164051(n) in base 2.

101, 10010, 1000100, 100001000, 10000010000, 1000000100000, 100000001000000, 10000000010000000, 1000000000100000000, 100000000001000000000

Offset: 1

Author

Jaroslav Krizek, Aug 14 2009

Keywords

• nonn
• base
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (110,-1000).

Programs

Mathematica

Table[FromDigits@ IntegerDigits[2^(2 n) + 2^(n - 1), 2], {n, 12}] (* or *)
Rest@ CoefficientList[Series[x (101 - 1100 x)/((1 - 10 x) (1 - 100 x)), {x, 0, 12}], x] (* Michael De Vlieger, Jun 21 2016 *)

PARI

x='x+O('x^50); Vec(x*(101 - 1100*x)/((1 - 10*x)*(1 - 100*x))) \\ G. C. Greubel, Sep 15 2017

Formula

a(n) = 10^(2*n) + 10^(n-1). The digits from the left to the right: number 1, n times 0, number 1, and (n-1) times 0.

From Chai Wah Wu, Jun 20 2016: (Start)

a(n) = 110*a(n-1) - 1000*a(n-2) for n > 2.

G.f.: x*(101 - 1100*x)/((1 - 10*x)*(1 - 100*x)). (End)

E.g.f.: (-11 + exp(10*x) + 10*exp(100*x))/10. - Ilya Gutkovskiy, Jun 21 2016

Extensions

Edited by Charles R Greathouse IV, Oct 12 2009