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.

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

1,7

Links

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

Example

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;
  ...

Prog

(PARI) \\ 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; ) }

Crossrefs

Row sums are A303835.

Column 1 is A005418(n-2).

Cf. A302828, A303869.

Sequence in context: A368605 A334715 A026105 * A060475 A168069 A334014

Adjacent sequences: A303865 A303866 A303867 * A303869 A303870 A303871

Keyword

nonn,tabl

Author

Andrew Howroyd, May 01 2018

Status

approved