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.

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

1,7

Links

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

Example

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;
  ...

Prog

(PARI) \\ 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; )}

Crossrefs

Row sums are A303836.

Column 1 is A051437(n-3).

Cf. A303844, A303732, A303864, A303868.

Sequence in context: A227216 A239678 A136374 * A081246 A264928 A323874

Adjacent sequences: A303866 A303867 A303868 * A303870 A303871 A303872

Keyword

nonn,tabl

Author

Andrew Howroyd, May 01 2018

Status

approved