A152775 Numbers with 3n binary digits where every run length is 3, written in binary.

111, 111000, 111000111, 111000111000, 111000111000111, 111000111000111000, 111000111000111000111, 111000111000111000111000, 111000111000111000111000111, 111000111000111000111000111000

Offset: 1

Author

Omar E. Pol, Jan 18 2009

Keywords

• easy
• nonn
• base

Comments

A152776 written in base 2.

Examples

			n ... a(n) .............. A152776(n)
1 ... 111 ............... 7
2 ... 111000 ............ 56
3 ... 111000111 ......... 455
4 ... 111000111000 ...... 3640
5 ... 111000111000111 ... 29127
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..100
• Index entries for linear recurrences with constant coefficients, signature (1000,1,-1000).

Crossrefs

Cf. A043291, A153435, A152776.

Programs

Mathematica

FromDigits/@Table[Flatten[PadRight[{},n,{a,b}]/.{a->{1,1,1},b->{0,0,0}}],{n,10}] (* Harvey P. Dale, Mar 23 2012 *)
CoefficientList[Series[111/((x - 1) (x + 1) (1000 x - 1)), {x, 0, 20}], x] (* Vincenzo Librandi, Apr 21 2014 *)

PARI

Vec(111*x / ((x-1)*(x+1)*(1000*x-1)) + O(x^100)) \\ Colin Barker, Apr 20 2014

Formula

From Colin Barker, Apr 20 2014: (Start)

a(n) = (-1001-999*(-1)^n+2^(4+3*n)*125^(1+n))/18018.

a(n) = 1000*a(n-1)+a(n-2)-1000*a(n-3).

G.f.: 111*x / ((x-1)*(x+1)*(1000*x-1)). (End).