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A291371 Number of maximal chord diagrams of genus g counted up to rotations and reflections. 1

%I

%S 1,4,82,7258,1491629,506855279,254118439668,176377605783906,

%T 162019808170348933,190375587419231088550,278587959330563466969926,

%U 496903413656110608290219603

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

%C 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 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 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 (Python 2.7)

%o rot_sym = [

%o 0, 1, 4, 131, 14118, 2976853, 1013582110, 508233789579, 352755124921122,

%o 324039613564554401, 380751174738424280720, 557175918657122229139987,

%o 993806827312044893602464496, # A291172

%o ]

%o def u(n):

%o if n < 0:

%o return 0

%o if n <= 1:

%o return 1

%o sum = 0

%o sum -= (4 * n - 1) * u(n - 1)

%o sum += n * (2 * n - 3) * (10 * n - 9) * u(n - 2)

%o sum += 5 * (2 * n - 3) * (2 * n - 4) * (2 * n - 5) * u(n - 3)

%o sum -= 2 * (2 * n - 3) * (2 * n - 4) * (2 * n - 5) * (2 * n - 6) * (2 * n - 7) * u(n - 4)

%o return sum / (n + 1)

%o for i in range(1, 13):

%o print (2 * rot_sym[i] + u(i) + u(i - 1) * (2 * i - 1)) / 4

%Y Maximal diagrams up to rotations: A291172.

%K nonn

%O 1,2

%A _Evgeniy Krasko_, Sep 03 2017

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Last modified September 28 08:33 EDT 2020. Contains 337394 sequences. (Running on oeis4.)