cp's OEIS Frontend

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.

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

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%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