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
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).
Programs
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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
Comments