%I #27 Apr 20 2024 10:23:19
%S 11111,1111100000,111110000011111,11111000001111100000,
%T 1111100000111110000011111,111110000011111000001111100000,
%U 11111000001111100000111110000011111,1111100000111110000011111000001111100000,111110000011111000001111100000111110000011111
%N Numbers with 5n binary digits where every run length is 5, written in binary.
%C A154808 written in base 2.
%H Vincenzo Librandi, <a href="/A154807/b154807.txt">Table of n, a(n) for n = 1..100</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (100000,1,-100000).
%F From _Colin Barker_, Apr 20 2014: (Start)
%F a(n) = (-100001-99999*(-1)^n+2^(6+5*n)*3125^(1+n))/1800018.
%F a(n) = 100000*a(n-1)+a(n-2)-100000*a(n-3).
%F G.f.: 11111*x / ((x-1)*(x+1)*(100000*x-1)). (End)
%e n ... a(n) ........................ A154808(n)
%e 1 ... 11111 ....................... 31
%e 2 ... 1111100000 .................. 992
%e 3 ... 111110000011111 ............. 31775
%e 4 ... 11111000001111100000 ........ 1016800
%e 5 ... 1111100000111110000011111 ... 32537631
%t CoefficientList[Series[11111/((x - 1) (x + 1) (100000 x - 1)), {x, 0, 10}], x] (* _Vincenzo Librandi_, Apr 22 2014 *)
%t LinearRecurrence[{100000,1,-100000},{11111,1111100000,111110000011111},20] (* _Harvey P. Dale_, Aug 08 2023 *)
%o (PARI) Vec(11111*x/((x-1)*(x+1)*(100000*x-1)) + O(x^100)) \\ _Colin Barker_, Apr 20 2014
%Y Cf. A152775, A153435, A154805, A154808.
%K easy,nonn,base
%O 1,1
%A _Omar E. Pol_, Jan 25 2009
%E More terms from _Colin Barker_, Apr 20 2014