A303836 -id:A303836 - cp's OEIS frontend

A303844 Number of noncrossing path sets on n nodes up to rotation with each path having at least two nodes.

1, 0, 1, 1, 4, 7, 26, 69, 246, 818, 2976, 10791, 40591, 153959, 594753, 2320696, 9159498, 36467012, 146411208, 592046830, 2409946566, 9867745442, 40623068380, 168058068487, 698400767839, 2914407151002, 12208398647345, 51322369218674, 216463504458521

Offset: 0

Andrew Howroyd, May 01 2018

nonn

			Case n=4: There are 4 possibilities:
.
   o---o   o   o   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, A303732, A303836, A303839.

\\ See A303732 for NCPathSetsModCyclic
Vec(NCPathSetsModCyclic(vector(30, k, k>1)))

A303869 Triangle read by rows: T(n,k) = number of noncrossing path sets on n nodes up to rotation with k paths and isolated vertices allowed.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 3, 4, 2, 1, 4, 11, 8, 2, 1, 10, 34, 39, 16, 3, 1, 16, 92, 144, 90, 25, 3, 1, 36, 256, 545, 473, 197, 40, 4, 1, 64, 672, 1878, 2184, 1246, 370, 56, 4, 1, 136, 1762, 6296, 9436, 7130, 2910, 658, 80, 5, 1, 256, 4480, 20100, 38025, 36690, 19698, 6090, 1080, 105, 5, 1

Offset: 1

Andrew Howroyd, May 01 2018

			Triangle begins:
    1;
    1,    1;
    1,    1,    1;
    3,    4,    2,    1;
    4,   11,    8,    2,    1;
   10,   34,   39,   16,    3,    1;
   16,   92,  144,   90,   25,    3,   1;
   36,  256,  545,  473,  197,   40,   4,  1;
   64,  672, 1878, 2184, 1246,  370,  56,  4, 1;
  136, 1762, 6296, 9436, 7130, 2910, 658, 80, 5, 1;
  ...

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

Row sums are A303836.
Column 1 is A051437(n-3).
Cf. A303844, A303732, A303864, A303868.

\\ See A303732 for NCPathSetsModCyclic
{ my(rows=Vec(NCPathSetsModCyclic(vector(10, k, y))-1));
for(n=1, #rows, for(k=1,n,print1(polcoeff(rows[n],k), ", ")); print;)}

cp's OEIS Frontend

A303844 Number of noncrossing path sets on n nodes up to rotation with each path having at least two nodes.

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