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 A234717 #18 Nov 23 2023 18:00:02
%S A234717 1,7,16,30,47,69,94,124,157,195,236,282,331,385,442,504,569,639,712,
%T A234717 790,871,957,1046,1140,1237,1339,1444,1554,1667,1785,1906,2032,2161,
%U A234717 2295,2432,2574,2719,2869,3022,3180,3341,3507
%N A234717 a(n) = floor(n/(exp(1/(2*n))-1)).
%C A234717 Equations of this general form: (n/(exp(1/(r*n))-1)) have a fractional portion that converges to one or more rational fractions if r is rational. They have second differences that are nearly constant before the floor function, and repeat in patterns when calculated after the floor function.
%C A234717 The fractional portion of this equation (before the floor function) oscillates between two fractions that converge towards 1/24 and 13/24.
%C A234717 Second differences of a(n) = repeat{3,5}.
%C A234717 First differences of a(n) = A075123(n+3).
%C A234717 Partial sums of a(n) = A033951(n).
%H A234717 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A234717 From _Ralf Stephan_, Mar 28 2014: (Start)
%F A234717 a(n) = (1/4)*(8n^2 - 2n - 1 + (-1)^n).
%F A234717 G.f.: x*(2*x^2 + 5*x + 1)/((1-x^2)*(1-x)^2). (End)
%F A234717 a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4). - _Wesley Ivan Hurt_, Apr 01 2022
%F A234717 E.g.f.: (x*(4*x + 3)*cosh(x) + (4*x^2 + 3*x - 1)*sinh(x))/2. - _Stefano Spezia_, Nov 23 2023
%t A234717 Table[Floor[n/(Exp[1/(2 n)] - 1)], {n, 100}] (* _Wesley Ivan Hurt_, Apr 01 2022 *)
%Y A234717 Cf. A033951, A075123.
%K A234717 nonn,easy
%O A234717 1,2
%A A234717 _Richard R. Forberg_, Dec 29 2013