cp's OEIS Frontend

A291371 Number of maximal chord diagrams of genus g counted up to rotations and reflections.

%I A291371 #35 Jan 15 2025 20:09:29
%S A291371 1,4,82,7258,1491629,506855279,254118439668,176377605783906,
%T A291371 162019808170348933,190375587419231088550,278587959330563466969926,
%U A291371 496903413656110608290219603
%N A291371 Number of maximal chord diagrams of genus g counted up to rotations and reflections.
%C A291371 Also the number of non-isomorphic one-face one-vertex maps on a genus g surface where both orientation-preserving and orientation-reversing isomorphisms are taken into account.
%H A291371 Evgeniy Krasko, <a href="https://arxiv.org/abs/1709.00796">Counting Unlabelled Chord Diagrams of Maximal Genus</a>, arXiv:1709.00796 [math.CO], 2017.
%H A291371 Evgeny Krasko, A. Omelchenko, <a href="http://arxiv.org/abs/1601.05073">Enumeration of Chord Diagrams without Loops and Parallel Chords</a>, arXiv preprint arXiv:1601.05073 [math.CO], 2016; Electronic Journal of Combinatorics 24(3) (2017), #P3.43
%o A291371 (Python) # Python version 2.7
%o A291371 rot_sym = [
%o A291371   0, 1, 4, 131, 14118, 2976853, 1013582110, 508233789579, 352755124921122,
%o A291371   324039613564554401, 380751174738424280720, 557175918657122229139987,
%o A291371   993806827312044893602464496, # A291172
%o A291371 ]
%o A291371 def u(n):
%o A291371   if n < 0:
%o A291371     return 0
%o A291371   if n <= 1:
%o A291371     return 1
%o A291371   sum = 0
%o A291371   sum -= (4 * n - 1) * u(n - 1)
%o A291371   sum += n * (2 * n - 3) * (10 * n - 9) * u(n - 2)
%o A291371   sum += 5 * (2 * n - 3) * (2 * n - 4) * (2 * n - 5) * u(n - 3)
%o A291371   sum -= 2 * (2 * n - 3) * (2 * n - 4) * (2 * n - 5) * (2 * n - 6) * (2 * n - 7) * u(n - 4)
%o A291371   return sum / (n + 1)
%o A291371 for i in range(1, 13):
%o A291371   print (2 * rot_sym[i] + u(i) + u(i - 1) * (2 * i - 1)) / 4
%Y A291371 Maximal diagrams up to rotations: A291172.
%K A291371 nonn
%O A291371 1,2
%A A291371 _Evgeniy Krasko_, Sep 03 2017