%I #27 Sep 02 2024 00:19:39
%S 0,0,1,0,1,1,1,0,2,1,1,2,1,1,5,0,1,5,1,2,10,1,1,12,4,1,23,2,1,38,1,0,
%T 64,1,12,102,1,1,191,12,1,329,1,2,633,1,1,1088,9,34,2057,2,1,3771,66,
%U 12,7156,1,1,13464,1,1,25503,0,193,48179,1,2,92206,358,1,175792,1,1,338202
%N Number of incongruent n-sided periodic Reinhardt polygons.
%H Kevin G. Hare and Michael J. Mossinghoff, <a href="https://doi.org/10.1007/s00454-012-9479-">Sporadic Reinhardt Polygons</a>, Discrete & Computational Geometry. An International Journal of Mathematics and Computer Science 49, no. 3 (2013): 540-57.
%H Kevin G. Hare and Michael J. Mossinghoff, <a href="https://doi.org/10.1007/s10711-018-0326-5">Most Reinhardt Polygons Are Sporadic</a>, Geom. Dedicata 198 (2019): 1-18.
%H Michael J. Mossinghoff, <a href="https://doi.org/10.1016/j.jcta.2011.03.004">Enumerating Isodiametric and Isoperimetric Polygons</a>, J. Combin. Theory Ser. A 118, no. 6 (2011): 1801-15.
%H Michael Mossinghoff, <a href="https://icerm.brown.edu/materials/Slides/sw-14-1/Reinhardt_Polygons_%5D_Michael_Mossinghoff.pdf">I love Reinhardt Polygons</a>, ICERM 2014.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Reinhardt_polygon">Reinhardt polygon</a>
%F a(n) = A374832(n) - A373695(n).
%F a(n) = Sum_{d|n, d>1} D(n/d)*Mu(2d), with D(m) = 2^floor((m-3)/2) + (Sum_{d|m, d odd} 2^(m/d)*Phi(d) )/(4m), where Mu is MoebiusMu and Phi is EulerPhi.
%t dD[m_] := 2^Floor[(m - 3)/2] + Sum[2^(m/d) EulerPhi[d], {d, DeleteCases[Divisors[m], _?EvenQ]}]/4/m;
%t a[n_] := Sum[dD[n/d] MoebiusMu[2 d], {d, DeleteCases[Divisors[n], 1]}];
%Y Cf. A000010, A008683, A374832, A373695.
%K nonn
%O 1,9
%A _Bernd Mulansky_, Aug 04 2024