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 A363773 #68 Jun 29 2023 10:08:54
%S A363773 1,2,7,26,103,410,1639,6554,26215,104858,419431,1677722,6710887,
%T A363773 26843546,107374183,429496730,1717986919,6871947674,27487790695,
%U A363773 109951162778,439804651111,1759218604442,7036874417767,28147497671066,112589990684263,450359962737050
%N A363773 a(n) = (4^(n+1) + (-1)^n + 5)/10.
%C A363773 a(n) is a part of the numerator of the approximate solutions x(n) = (Pi/2)*(1+5/((4^(n+1)-(-1)^(n+1)))) = a(n)*Pi/A015521(n+1) of D_d(exp(-i*x(n))) = Cl_d(x(n)+Pi) = 0, where D_d(exp(-i*x(n))) is the Bloch-Wigner-Ramakrishnan polylogarithm function and Cl_d(x(n)+Pi) is the Clausen function for odd d >= 3 and n >= 0.
%H A363773 Paolo Xausa, <a href="/A363773/b363773.txt">Table of n, a(n) for n = 0..1000</a>
%H A363773 Evangelos G. Filothodoros, Anastasios C. Petkou, and Nicholas D. Vlachos, <a href="https://doi.org/10.1016/j.nuclphysb.2019.01.015">The fermion-boson map for large d</a>, Nuclear Physics B, Volume 941, 2019, pp. 195-224.
%H A363773 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,1,-4).
%F A363773 a(n) = 1 + A037481(n).
%F A363773 G.f.: (1-2*x-2*x^2)/((x-1)*(4*x-1)*(x+1)).
%F A363773 E.g.f.: (4*e^(4*x) + e^-x + 5*e^x)/10.
%t A363773 A363773list[nmax_]:=LinearRecurrence[{4,1,-4},{1,2,7},nmax+1];A363773list[50] (* _Paolo Xausa_, Jun 29 2023 *)
%o A363773 (Python)
%o A363773 def A363773(n): return (1<<(n<<1|1))//5+1 # _Chai Wah Wu_, Jun 28 2023
%Y A363773 Cf. A015521, A037481.
%K A363773 nonn,easy
%O A363773 0,2
%A A363773 _Evangelos G. Filothodoros_, Jun 21 2023