A303835 -id:A303835 - cp's OEIS frontend

A303839 Number of noncrossing path sets on n nodes up to rotation and reflection with each path having at least two nodes.

1, 0, 1, 1, 3, 5, 17, 40, 138, 430, 1546, 5478, 20525, 77310, 298301, 1161692, 4583525, 18239037, 73221198, 296046399, 1205038270, 4933969005, 20311807087, 84029440358, 349201537324, 1457205298510, 6104204225832, 25661191956781, 108231773165825

Offset: 0

Andrew Howroyd, May 01 2018

nonn

			Case n=4: There are 3 possibilities:
.
   o---o   o   o   o---o
           |   |     /
   o---o   o---o   o---o
.

Andrew Howroyd, Table of n, a(n) for n = 0..200

Cf. A303730, A303731, A303835, A303844.

\\ See A303731 for NCPathSetsModDihedral
Vec(NCPathSetsModDihedral(vector(30, k, k>1)))

A303868 Triangle read by rows: T(n,k) = number of noncrossing path sets on n nodes up to rotation and reflection with k paths and isolated vertices allowed.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 3, 2, 1, 3, 7, 6, 2, 1, 6, 20, 23, 11, 3, 1, 10, 50, 80, 51, 17, 3, 1, 20, 136, 285, 252, 109, 26, 4, 1, 36, 346, 966, 1119, 652, 200, 36, 4, 1, 72, 901, 3188, 4782, 3623, 1502, 352, 50, 5, 1, 136, 2264, 10133, 19116, 18489, 9949, 3120, 570, 65, 5, 1

Offset: 1

Andrew Howroyd, May 01 2018

			Triangle begins:
   1;
   1,   1;
   1,   1,    1;
   2,   3,    2,    1;
   3,   7,    6,    2,    1;
   6,  20,   23,   11,    3,    1;
  10,  50,   80,   51,   17,    3,   1;
  20, 136,  285,  252,  109,   26,   4,  1;
  36, 346,  966, 1119,  652,  200,  36,  4, 1;
  72, 901, 3188, 4782, 3623, 1502, 352, 50, 5, 1;
  ...

Andrew Howroyd, Table of n, a(n) for n = 1..1275

Row sums are A303835.
Column 1 is A005418(n-2).
Cf. A302828, A303869.

\\ See A303731 for NCPathSetsModDihedral
{ my(rows=Vec(NCPathSetsModDihedral(vector(10, k, y))-1));
  for(n=1, #rows, for(k=1, n, print1(polcoeff(rows[n],k), ", ")); print;) }

cp's OEIS Frontend

A303839 Number of noncrossing path sets on n nodes up to rotation and reflection with each path having at least two nodes.

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