A303868 - OEIS

%I #8 May 03 2018 14:55:51

%S 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,

%T 136,285,252,109,26,4,1,36,346,966,1119,652,200,36,4,1,72,901,3188,

%U 4782,3623,1502,352,50,5,1,136,2264,10133,19116,18489,9949,3120,570,65,5,1

%N 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.

%H Andrew Howroyd, <a href="/A303868/b303868.txt">Table of n, a(n) for n = 1..1275</a>

%e Triangle begins:

%e    1;

%e    1,   1;

%e    1,   1,    1;

%e    2,   3,    2,    1;

%e    3,   7,    6,    2,    1;

%e    6,  20,   23,   11,    3,    1;

%e   10,  50,   80,   51,   17,    3,   1;

%e   20, 136,  285,  252,  109,   26,   4,  1;

%e   36, 346,  966, 1119,  652,  200,  36,  4, 1;

%e   72, 901, 3188, 4782, 3623, 1502, 352, 50, 5, 1;

%e   ...

%o (PARI) \\ See A303731 for NCPathSetsModDihedral

%o { my(rows=Vec(NCPathSetsModDihedral(vector(10, k, y))-1));

%o   for(n=1, #rows, for(k=1, n, print1(polcoeff(rows[n],k), ", ")); print;) }

%Y Row sums are A303835.

%Y Column 1 is A005418(n-2).

%Y Cf. A302828, A303869.

%K nonn,tabl

%O 1,7

%A _Andrew Howroyd_, May 01 2018