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A303835 Number of noncrossing path sets on n nodes up to rotation and reflection with isolated vertices allowed.

%I A303835 #12 May 03 2018 17:04:25
%S A303835 1,1,2,3,8,19,64,212,833,3360,14476,63848,289892,1338000,6275589,
%T A303835 29791100,142973014,692507861,3382070233,16638445745,82395500651,
%U A303835 410463736691,2055858519575,10347925039015,52321093290715,265648012207312,1353953547877556,6925400869302520
%N A303835 Number of noncrossing path sets on n nodes up to rotation and reflection with isolated vertices allowed.
%H A303835 Andrew Howroyd, <a href="/A303835/b303835.txt">Table of n, a(n) for n = 0..200</a>
%e A303835 Case n=3: There are 3 possibilities:
%e A303835 .
%e A303835      o        o       o
%e A303835                      / \
%e A303835    o   o    o---o   o   o
%e A303835 .
%e A303835 Case n=4: There are 8 possibilities:
%e A303835 .
%e A303835    o   o    o   o    o   o    o   o    o   o    o---o    o   o    o---o
%e A303835                        /      |          /               |   |      /
%e A303835    o   o    o---o    o   o    o---o    o---o    o---o    o---o    o---o
%e A303835 .
%o A303835 (PARI) \\ See A303731 for NCPathSetsModDihedral
%o A303835 Vec(NCPathSetsModDihedral(vector(30, k, 1)))
%Y A303835 Cf. A303731, A303839.
%K A303835 nonn
%O A303835 0,3
%A A303835 _Andrew Howroyd_, May 01 2018