This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A154807 #27 Apr 20 2024 10:23:19 %S A154807 11111,1111100000,111110000011111,11111000001111100000, %T A154807 1111100000111110000011111,111110000011111000001111100000, %U A154807 11111000001111100000111110000011111,1111100000111110000011111000001111100000,111110000011111000001111100000111110000011111 %N A154807 Numbers with 5n binary digits where every run length is 5, written in binary. %C A154807 A154808 written in base 2. %H A154807 Vincenzo Librandi, <a href="/A154807/b154807.txt">Table of n, a(n) for n = 1..100</a> %H A154807 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (100000,1,-100000). %F A154807 From _Colin Barker_, Apr 20 2014: (Start) %F A154807 a(n) = (-100001-99999*(-1)^n+2^(6+5*n)*3125^(1+n))/1800018. %F A154807 a(n) = 100000*a(n-1)+a(n-2)-100000*a(n-3). %F A154807 G.f.: 11111*x / ((x-1)*(x+1)*(100000*x-1)). (End) %e A154807 n ... a(n) ........................ A154808(n) %e A154807 1 ... 11111 ....................... 31 %e A154807 2 ... 1111100000 .................. 992 %e A154807 3 ... 111110000011111 ............. 31775 %e A154807 4 ... 11111000001111100000 ........ 1016800 %e A154807 5 ... 1111100000111110000011111 ... 32537631 %t A154807 CoefficientList[Series[11111/((x - 1) (x + 1) (100000 x - 1)), {x, 0, 10}], x] (* _Vincenzo Librandi_, Apr 22 2014 *) %t A154807 LinearRecurrence[{100000,1,-100000},{11111,1111100000,111110000011111},20] (* _Harvey P. Dale_, Aug 08 2023 *) %o A154807 (PARI) Vec(11111*x/((x-1)*(x+1)*(100000*x-1)) + O(x^100)) \\ _Colin Barker_, Apr 20 2014 %Y A154807 Cf. A152775, A153435, A154805, A154808. %K A154807 easy,nonn,base %O A154807 1,1 %A A154807 _Omar E. Pol_, Jan 25 2009 %E A154807 More terms from _Colin Barker_, Apr 20 2014