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Number of noncrossing path sets on n nodes up to rotation with isolated vertices allowed.
3

%I #16 May 03 2018 17:03:29

%S 1,1,2,3,10,26,103,371,1552,6475,28414,126530,577188,2670332,12538434,

%T 59554199,285882600,1384875627,6763821250,33276183371,164789380052,

%U 820923863918,4111708742153,20695831549310,104642143845428,531295928725508,2707906874407464

%N Number of noncrossing path sets on n nodes up to rotation with isolated vertices allowed.

%H Andrew Howroyd, <a href="/A303836/b303836.txt">Table of n, a(n) for n = 0..200</a>

%e Case n=4: There are 10 possibilities:

%e .

%e o o o o o o o o o---o

%e / |

%e o o o---o o o o---o o---o

%e .

%e o o o o o o o---o o---o

%e / \ | | / \

%e o---o o---o o---o o---o o---o

%e .

%o (PARI) \\ See A303732 for NCPathSetsModCyclic

%o Vec(NCPathSetsModCyclic(vector(30, k, 1)))

%Y Row sums of A303869.

%Y Cf. A303732, A303844.

%K nonn

%O 0,3

%A _Andrew Howroyd_, May 01 2018