A153435 Numbers with 2n binary digits where every run length is 2, written in binary.

11, 1100, 110011, 11001100, 1100110011, 110011001100, 11001100110011, 1100110011001100, 110011001100110011, 11001100110011001100, 1100110011001100110011, 110011001100110011001100

Offset: 1

Author

Omar E. Pol, Dec 26 2008

Keywords

• easy
• nonn
• base

Comments

A043291 written in base 2.

Examples

			n ... a(n) ....... A043291(n)
1 ... 11 ............. 3
2 ... 1100 .......... 12
3 ... 110011 ........ 51
4 ... 11001100 ..... 204
5 ... 1100110011 ... 819
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (100,1,-100).

Crossrefs

Cf. A043291.

Programs

Maple

A153435:=n->(-101-99*(-1)^n+2^(3+2*n)*25^(1+n))/1818; seq(A153435(n), n=1..20); # Wesley Ivan Hurt, Apr 19 2014

Mathematica

Table[(-101 - 99*(-1)^n + 2^(3 + 2*n)*25^(1 + n))/1818, {n, 20}] (* Wesley Ivan Hurt, Apr 19 2014 *)
CoefficientList[Series[11/((x - 1) (x + 1) (100 x - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Apr 20 2014 *)

PARI

Vec(11*x / ((x-1)*(x+1)*(100*x-1)) + O(x^100)) \\ Colin Barker, Apr 19 2014

Formula

From Colin Barker, Apr 19 2014: (Start)

a(n) = (-101-99*(-1)^n+2^(3+2*n)*25^(1+n))/1818.

a(n) = 100*a(n-1)+a(n-2)-100*a(n-3).

G.f.: 11*x / ((x-1)*(x+1)*(100*x-1)).(End).