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 A229297 #29 Jan 01 2023 02:29:13
%S A229297 1,0,1,2,1,0,1,0,3,0,1,2,1,0,1,4,1,0,1,2,1,0,1,0,5,0,3,2,1,0,1,0,1,0,
%T A229297 1,6,1,0,1,0,1,0,1,2,3,0,1,4,7,0,1,2,1,0,1,0,1,0,1,2,1,0,3,8,1,0,1,2,
%U A229297 1,0,1,0,1,0,5,2,1,0,1,4,9,0,1,2,1,0
%N A229297 Number of solutions to x^2 == n (mod 2*n) for 0 <= x < 2*n.
%H A229297 Andrew Howroyd, <a href="/A229297/b229297.txt">Table of n, a(n) for n = 1..10000</a>
%F A229297 From _Andrew Howroyd_, Aug 07 2018: (Start)
%F A229297 Multiplicative with a(2^e) = 0 for odd e and 2^floor(e/2) for even e, and a(p^e) = p^floor(e/2) for p>=3. [corrected by _Georg Fischer_, Aug 01 2022].
%F A229297 a(n) = A000188(n) for odd n, a(2^k) = 1 + (-1)^k for k > 0. (End)
%F A229297 From _Amiram Eldar_, Jan 01 2023: (Start)
%F A229297 Dirichlet g.f.: zeta(2*s-1)*zeta(s)/(zeta(2*s)*(1+1/2^s)).
%F A229297 Sum_{k=1..n} a(k) ~ (n*log(n) + (3*gamma + log(2)/3 - 2*zeta'(2)/zeta(2) - 1)*n)*2/Pi^2, where gamma is Euler's constant (A001620). (End)
%t A229297 A[n_] := Sum[If[Mod[a^2, 2*n] == n, 1, 0], {a, 0, 2*n - 1}]; Array[A, 100]
%t A229297 f[p_, e_] := If[OddQ[e], p^((e - 1)/2), p^(e/2)]; f[2, e_] := If[OddQ[e], 0, 2^(e/2)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* _Amiram Eldar_, Jan 01 2023 *)
%o A229297 (PARI) a(n)={sum(i=0, 2*n-1, i^2%(2*n)==n)} \\ _Andrew Howroyd_, Aug 06 2018
%o A229297 (PARI) a(n)={if(valuation(n,2)%2==1, 0, core(n, 1)[2])} \\ _Andrew Howroyd_, Aug 07 2018
%Y A229297 Cf. A000188, A001620, A229294, A229295, A229296.
%K A229297 nonn,mult
%O A229297 1,4
%A A229297 _José María Grau Ribas_, Sep 22 2013