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

Author

Omar E. Pol, Jan 25 2009

Keywords

• easy
• nonn
• base

Comments

A154808 written in base 2.

Examples

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..100
• Index entries for linear recurrences with constant coefficients, signature (100000,1,-100000).

Crossrefs

Cf. A152775, A153435, A154805, A154808.

Programs

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 *)

PARI

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

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)

Extensions

More terms from Colin Barker, Apr 20 2014