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.

A110595 a(1)=5. For n > 1, a(n) = 4*5^(n-1) = A005054(n).

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%I A110595 #35 Jun 29 2023 12:30:19
%S A110595 5,20,100,500,2500,12500,62500,312500,1562500,7812500,39062500,
%T A110595 195312500,976562500,4882812500,24414062500,122070312500,610351562500,
%U A110595 3051757812500,15258789062500,76293945312500,381469726562500
%N A110595 a(1)=5. For n > 1, a(n) = 4*5^(n-1) = A005054(n).
%C A110595 a(n) is the number of n-digit integers that contain only even digits (A014263). - _Bernard Schott_, Nov 11 2022
%H A110595 G. C. Greubel, <a href="/A110595/b110595.txt">Table of n, a(n) for n = 1..1000</a>
%H A110595 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (5).
%F A110595 O.g.f.: 5*x*(1-x)/(1-5*x). - Better definition from _R. J. Mathar_, May 13 2008
%F A110595 Sum_{n>=1} 1/a(n) = 21/80. - _Bernard Schott_, Nov 11 2022
%t A110595 Join[{5},NestList[5#&,20,20]] (* _Harvey P. Dale_, Jun 19 2013 *)
%t A110595 Rest[CoefficientList[Series[5 x (1 - x)/(1 - 5 x), {x,0,50}], x]] (* _G. C. Greubel_, Sep 01 2017 *)
%o A110595 (PARI) my(x='x+O('x^50)); Vec(5*x*(1-x)/(1-5*x)) \\ _G. C. Greubel_, Sep 01 2017
%Y A110595 Cf. A000351, A007091, A014263, A081604, A110591, A110592, A110593, A110594.
%K A110595 easy,less,nonn
%O A110595 1,1
%A A110595 _Jonathan Vos Post_, Jul 29 2005
%E A110595 Better definition from _R. J. Mathar_, May 13 2008
%E A110595 Incorrect comment removed by _Michel Marcus_, Nov 11 2022