A154807 Numbers with 5n binary digits where every run length is 5, written in binary.

11111, 1111100000, 111110000011111, 11111000001111100000, 1111100000111110000011111, 111110000011111000001111100000, 11111000001111100000111110000011111, 1111100000111110000011111000001111100000, 111110000011111000001111100000111110000011111

Offset

1,1

Comments

A154808 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 (100000,1,-100000).

Formula

From Colin Barker, Apr 20 2014: (Start)

a(n) = (-100001-99999*(-1)^n+2^(6+5*n)*3125^(1+n))/1800018.

a(n) = 100000*a(n-1)+a(n-2)-100000*a(n-3).

G.f.: 11111*x / ((x-1)*(x+1)*(100000*x-1)). (End)

Example

n ... a(n) ........................ A154808(n)
1 ... 11111 ....................... 31
2 ... 1111100000 .................. 992
3 ... 111110000011111 ............. 31775
4 ... 11111000001111100000 ........ 1016800
5 ... 1111100000111110000011111 ... 32537631

Mathematica

CoefficientList[Series[11111/((x - 1) (x + 1) (100000 x - 1)), {x, 0, 10}], x] (* Vincenzo Librandi, Apr 22 2014 *)
LinearRecurrence[{100000, 1, -100000}, {11111, 1111100000, 111110000011111}, 20] (* Harvey P. Dale, Aug 08 2023 *)

Prog

(PARI) Vec(11111*x/((x-1)*(x+1)*(100000*x-1)) + O(x^100)) \\ Colin Barker, Apr 20 2014

Crossrefs

Cf. A152775, A153435, A154805, A154808.

Sequence in context: A115810 A262497 A291946 * A076164 A234661 A261778

Adjacent sequences: A154804 A154805 A154806 * A154808 A154809 A154810

Keyword

easy,nonn,base,changed

Author

Omar E. Pol, Jan 25 2009

Extensions

More terms from Colin Barker, Apr 20 2014

Status

approved