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

1,1

Comments

A152776 written in base 2.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..100

Index entries for linear recurrences with constant coefficients, signature (1000,1,-1000).

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).

Example

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

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 *)

Prog

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

Crossrefs

Cf. A043291, A153435, A152776.

Sequence in context: A145698 A362920 A244845 * A362118 A242646 A242645

Adjacent sequences: A152772 A152773 A152774 * A152776 A152777 A152778

Keyword

easy,nonn,base

Author

Omar E. Pol, Jan 18 2009

Status

approved